David Moyes, the Everton manager, believes that competition for places could hold the key to success as the Barclays Premier League club step up their pursuit of Champions League qualification and European silverware.

Everton have applied to enter the Intertoto Cup next season as an alternative route into Europe, but, with his team fourth in the table and in the last 16 of the Uefa Cup, Moyes will hope that he does not have to rely on such an option.

The 2-0 victory over Manchester City on Monday opened a three-point gap between Everton and Liverpool, their Merseyside rivals, in fifth, while Moyes has also set his sights on winning the Uefa Cup. Everton travel to Italy next week for the first leg of their round-of-16 tie against Fiorentina.

“If we are going to challenge for trophies in the future, I honestly don’t think there can be a guaranteed place for anyone,” Moyes said. “We have got competition everywhere. The three central defenders [Joleon Lescott, Joseph Yobo and Phil Jagiel-ka] have been absolutely top drawer.”

With Tottenham Hotspur having claimed one of the three Uefa Cup places available to English teams after beating Chelsea in the Carling Cup final on Sunday, there is a chance of another spot going to an FA Cup finalist, unless Chelsea and Manchester United contest a second successive Wembley final in May. That would mean only the Premier League’s top five being guaranteed a European place next season.

“Clearly, European qualification through our league position or via the Uefa Cup is our main priority,” Keith Wyness, the Everton chief executive, said. “However, because of the deadline for Intertoto Cup applications, it would be remiss of us not to put our name forward.”

Fiorentina supporters have attempted to stoke the fires before their team’s match against Everton in Florence a week today by branding the Merseyside club’s supporters “hooligans” and “particularly infamous”.

Such claims fly in the face of the good behaviour demonstrated by Everton’s fans in Europe this season and have been labelled as “grossly hypocritical” by supporters’ groups, given the outbreaks of violence that have marred several Serie A matches over the past year.