The Spaniard believes his side have no room for error between now and the end of the season if they are to finish in the top four, having beaten Fulham 3-1 on Sunday
The Spaniard saw his side defeat Fulham 3-1 at Craven Cottage on Sunday to move within four points of the Gunners, whom they face next weekend.
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“We always embrace the challenge and we always enjoy playing at Goodison, believe me we've created an incredible relationship between the fans and the players,” the Spaniard told reporters.
“The fans have been patient with the way we want to play, we feel supported and we feel we've got a real advantage playing at home.
“We've got Arsenal, Manchester United, Manchester City and Crystal Palace so they are as difficult as they get but, even then, we feel that, if we can be perfect in what we do, we've got a great chance to get points and that's the way we're going to approach the final 7 games.”
Looking ahead to the game against the Gunners, Martinez acknowledged there is more pressure on Arsenal, as Everton have a game in hand on the north Londoners, but believes they will handle it.
"I think they cope with that expectation,” Martinez added. “They need to be coping with those expectations. I don't think that's an issue now.
“In fact, it's the opposite. If they would play without expectations I think that would be very difficult. I don't think it's a problem for Arsenal.”