Pressure increased on Roberto Martínez when Bill Kenwright revealed the new Everton manager's pledge to secure Champions League football at his unveiling last June. Ten months on the pressure is all on Arsenal, according to Martínez, thanks to the reaction of the "leaders" in the Everton dressing room to their chairman's unwitting declaration of intent.

Fourth place is in Everton's hands with five matches remaining, a sequence that commences against Crystal Palace at Goodison Park on Wednesday, following an outstanding run of seven consecutive league wins. The club last produced eight wins in succession when winning the title in 1985.

Martínez has delivered Everton's highest points total of the Premier League era in his first season in charge. Back in June, however, he was simply concerned with how Kenwright's admission of what was said at their interview would go down with David Moyes' former players.

"It has always been my vision that Everton would fight for Champions League football because of the history, the heritage and everything we have as a football club. We should be challenging for Champions League," said Martínez. "I think at the press conference it was a little bit too early to say we would be challenging because I hadn't even told my players about the vision, so I was sat there thinking 'I don't know how the players are going to react to this.'

"I expected to be the one to slowly unfold the plans, not just give it on the first day, and my worry was how the group would react. You have a new manager who walks in and says we're going to get into the Champions League, even though that has to be our aim long term. You always have to be driven by a vision at Everton, there are no excuses in football and you have to have that drive. He said it a little bit too early – it would have helped if he'd allowed me to say it to the players first.

"I think the reaction from the players would have been mixed. Some would say 'is that real?', others 'I don't mind that', and others would say 'we are ready for it'. That's where you get leaders and I think the leaders, the senior players, have been terrific in their reaction. Don't forget, we are on new ground, there are no two ways about it."

Martínez let the moment pass with Kenwright last summer, although he admits the Everton chairman has broached the subject frequently as the Spaniard's vision has taken shape. "I didn't say anything at the time because I have great respect for the chairman," he added. "When you meet him you realise his life is Everton and he has a genuine love for the football club.

"He has reminded me about it as the season has gone on because at the beginning he didn't believe it was possible. I would say it was three or four months into the season before he started to believe. It was the week we beat United and played so well at the Emirates, and then he said: 'Maybe I can see what you were saying.'"

Arsène Wenger said after reaching the FA Cup final on Saturday that Arsenal would secure their customary place in the Champions League with five straight league wins as Everton will drop points.

Martínez responded to that by saying: "There is no pressure on us. We have nothing to lose. I think the pressure comes when you have something to lose. We are in a position where we have everything to gain. We have already gained the club's highest points tally in Premier League history and that is an achievement. That is not easy in the modern game. So from this point on, we have everything to gain, and the only things I am focusing on are maintaining our standards and the competition for places.

"We are just going to enjoy the fight. If you had said Everton would be fourth in the table with five games to go at the beginning of the season, I don't think many people would have believed that. We are just enjoying the position, enjoying the challenge, and we want to finish as strong as we can."