The Latics currently occupy 18th place in the league after a recent run of form which has seen them pick up just one point from their last five games.
The corresponding fixture against Everton was drawn 2-2 at the DW Stadium in October and, when Martinez was asked if David Moyes' side were capable of finishing in a Champions League qualifying place this term, he was positive of their chances.
"Yes, because of the experience they have got and because of the way they have started the season," he told reporters.
|EVERTON TO APPEAL GIBSON RED
|13/2||Everton are 13/2 with bet365 to beat Wigan 2-0
"We all know that Everton traditionally start seasons a little bit slowly and then finish at a very good level.
"But we can speak from our own experience. It will be our second game against Everton and in the first one, it was the best Everton side we have faced.
"This Everton side tick every box. They have been able to get consistently good results in this league and that allows you to be fighting for the top four positions.
"At Goodison Park they are unbeaten and it is one of the hardest places to visit in the Premier League. We are well aware of all that, but we feel we can match Everton on our day."