One of the recurring themes from the recent We Are Evertonians evening at the Parklands Centre in which the club's two new ambassadors were unveiled were Everton's trophy successes. The event brought together two members of the last Championship-winning team from 1987 in the form of Ian Snodin and Graeme Sharp – the latter, of course, a winner of two League titles, an FA Cup and the European Cup Winners' Cup – and Graham Stuart who helped the Blues to their last trophy in 1995.

It brought home the rich history that runs through this football club but also painfully underscored just how long it has been since an Everton captain last lifted a piece of silverware. Pleasingly, from Roberto Martinez and CEO Robert Elstone to the ambassadors, there was a current of hunger and determination to end the current trophy drought as soon as possible running through their rhetoric. It has been far too long.

By May 2015, the earliest opportunity the Toffees can get their hands on some silverware, it will be 20 years since Everton last won a major competition. There are now adult Evertonians who have supported the club all their lives but never known the singular joy that is seeing your team win a trophy. In terms of time elapsed, the period between the title triumphs of 1939 and 1963 is longer but the interruption caused by the Second World War means that the current drought represents the greatest number of seasons without a trophy in the club's history.

It hints at the club's travails in the wake of the Heysel ban, the exodus of its best talent and the mis-management that allowed the club to languish while other clubs took advantage of the new era ushered in by BSykB after 1992. Indeed, the Blues were just minutes from tumbling through the trapdoor to what was then the First Division in 1994; but for the grace of the footballing gods, Barry Horne's right foot and the composure of Stuart, Everton's fall from grace might have been complete. It also speaks to the uneven playing field that has been fostered during the Premier League era, one in which only five teams have won the title in 21 years and, more importantly, far fewer clubs even have a shot at finishing top of the pile than was the case in the old Football League. As we know all too well, even the top four has become something of a closed shop.

The same skewed playing field bleeds through to the domestic cup tournaments as well, of course, but, by the very nature of knockout competition, there is greater opportunity in the League and FA Cups for teams outside the monied elite. Portsmouth and Wigan Athletic have demonstrated as much in recent years and Everton, of course, came very close to joining their ranks in 2009. That inability to hold on to Louis Saha's first-minute gift against Chelsea still hurts, as does the capitulation to Liverpool in the semi-finals three years later, while the failure to build on an impressive first leg performance in the Carling Cup in 2008 will also go down as a chance missed.

All three defeats hinted at the psychological barrier that David Moyes's teams seemed unable to overcome, one encapsulated in the former manager's failure to win away at any of Chelsea, Arsenal, Liverpool and Manchester United in his 11 years at the Goodison helm. An almost immediate resolution to defend that 1-0 lead at Wembley against Chelsea turned to near paralysis once it became clear that they were not going to be able to emulate the heroic defensive stand that won the FA Cup in '95. Similarly, self-belief appeared to drain from the team the instant Sylvain Distin's error had handed a poor Liverpool team the equaliser in 2012 and the match inevitably swung in the red horde's favour.

Though his team haven't yet hit the heights they did in his first season in charge, Martinez has instilled a more confident mindset in his players which has already resulted in a League double over United and some stirring performances against the old Sky Four at home and away. Unfortunately, while the tie could have gone either way, reality bit Everton in the FA Cup quarter finals at the Emirates Stadium last season when Arsenal knocked them out with a 4-1 scoreline.

Any hopes of ending the club's League Cup hoodoo have twice ended early under the Catalan, with both instances perpetuating a trend that had been firmly established under his predecessor where much-changed Everton teams made annoyingly premature exits from a competition that the club have never won. Implied prioritisation of progress in the League meant that unfamiliar line-ups were defeated in the cup, albeit in tricky away ties against Premier League opposition in the form of Fulham and Swansea City.

Striking that balance between the bread-and-butter of the League and what is the least glamourous of the four trophies Everton are in the running for has been particularly tricky this season. Juggling the Europa League with domestic commitments has been hard enough already given the injuries already affecting Martinez's squad without having the extra distraction of an extended run in the Capital One Cup. While it represents a potential route to silverware, there are no guarantees and Martinez has clearly highlighted progress in Europe as being more beneficial to his long-term goals. He's not alone; the fact that 10 different teams have won the League Cup since 2000 is evidence enough that plenty of our rivals have put the competition at the bottom of the list of priorities. On the flip side, however, that list if winners includes Leicester City, Birmingham City, Blackburn Rovers and Middlesbrough so it's hard not to feel that the Toffees have let a few good opportunities slip over the years.

Everton trophy timeline

Having retained a decent amount of its glamour despite the elevated profile of the Premier and Champions Leagues, the FA Cup has been a good deal more competitive and the mid-season break between the group phase and the knockout rounds of the Europa League should give Martinez the latitude to channel his energies and those of his players into improving on last season's run to the last eight when the Third Round kicks off in January. Certainly, his recent rhetoric suggests that he expects his team to start hitting its stride in the coming weeks to coincide with Everton's entry into the famous old competition where a few favourable draws and a run of victories would give him the opportunuty to win the trophy for the second time in his managerial career.

Of course, the Holy Grail is the Europa League because of the prize of a crack at the Champions League for the winner – the ultimate kill-two-birds-with-one-stone scenario for a club that has been trying to break through the glass ceiling on the home front for the better part of a decade. Depending on whether the winner of this season's Champions League final also qualifies for next year's competition via League placing at home, the holder of the 2014-15 Europa League title would go straight into the group stage of the big one in 2015-16. It's a long shot given the calibre of clubs that the Blues is likely to face in the rounds to come but there is no doubt that it's a gold-plated carrot should they be able to go all the way in Europe this season.

Encouragingly, when it's at something close to full-strength – as it conceivably could be by January if the current injury curse is laid to rest by then – this Everton side is capable of winning either cup. They have demonstrated that they can be a match for almost any team they might face domestically and Martinez's brand of passing football has looked very much at home in Europe this season where there is more space and fewer entrenched defences to break down. By their very nature, cup tournaments can be unpredictable and that can work both ways, but there is little question that the Blues are as well-equipped to land a trophy as they have been since the 1980s.

With every passing season, the craving for silverware at Everton grows so strong you can almost feel it leaching out of the girders at Goodison Park. The success that Roberto Martinez says is in our DNA has been dormant for too long now, suppressed by a combination of economic realities, psychology and, perhaps, the simple fact of the wrong man at the tiller. Martinez unquestionably "gets it" – what a trophy would mean to this club and its success-starved fans. Can he now find that vital mix of conviction, drive, fortune and desire to be the man to end the drought?