Roberto Martínez has said the freshness of Ross Barkley and Everton's younger players can help deliver the flawless finale he believes will be necessary for Champions League qualification.

The Everton manager last week predicted that one of the current top four would stumble during the run-in and Arsenal have subsequently dropped four points in two games, allowing Martínez's team to move to within six points of Arsène Wenger's side with a game in hand.

Everton take a four-match winning run in the Premier League to bottom-of-the-table Fulham and then face a demanding set of home fixtures – including Arsenal, Manchester United and Manchester City – before the end of the season. And the manager believes his team cannot afford to slip in their pursuit of the top four.

"We need a perfect finish," said Martínez. "The big advantage we have is an extra game on the others, which makes a big difference, and we've got City, United and Arsenal at home. That doesn't mean anything but if you're going to face these teams in the final third of the season you want to face them at home. We're just focusing on that and I still think if you get a certain amount of points [71] you've got a good chance of getting into the Champions League. I do feel if we finish strongly we'll have a great opportunity to do something special."

Barkley confirmed his return to form and fitness with a sensational goal in the 3-0 win at Newcastle United in midweek. Everton lost several creative talents to injury earlier in the year but their recovery, Martínez believes, has given the side added impetus.

He added: "As a manager you know if the season is getting a bit too long for you or when you're in a great moment and would love another 15 games, not just another eight. The way we planned this season was to finish the last 10 really strong from a physical point of view. I feel everyone is refreshed. I've tried to keep all the forward players fresh and in a good frame of mind, and think the young players have given us that unknown quantity. Having John Stones and Ross Barkley playing the way they've done, Gerard Deulofeu in that kind of form, we're starting to get a very strong young team with a lot of energy. That's why we're excited about having a strong run."

Everton's captain Phil Jagielka is in the squad for the trip to Craven Cottage having missed the previous five games with a hamstring problem.