The Toffees are having an impressive 2012-13, losing just twice in their 18 Barclays Premier League games so far and currently lie fifth in the table, behind fourth-placed Arsenal on goal difference alone.
Martinez is backing David Moyes' side to be challenging for a Champions League berth right up to the end of the campaign and expects a demanding assignment for the Latics on Merseyside, where Everton are unbeaten this term.
At the same time, though, the Spaniard is feeling optimistic ahead of the contest having seen his team only denied a home victory against Everton earlier this season when Leighton Baines' late penalty for the visitors ensured a 2-2 draw.
Asked if he thought the Toffees would be able to sustain their top-four push, Martinez said: "Yes, because of the experience they have got and because of the way they have started the season.
"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."
Wigan, currently 18th in the standings, could be boosted by the return of captain Gary Caldwell to their starting line-up on Wednesday.
Caldwell, recently sidelined by a hamstring problem, was back in the squad for Saturday's 1-0 home defeat to Arsenal as an unused substitute and will be monitored by Martinez ahead of the Everton game.
Fellow centre-back Ivan Ramis, who has also been nursing a hamstring complaint, has a chance of featuring as well, while midfielder James McCarthy (ankle) is a doubt.
"Gary Caldwell was in the squad on Saturday and he put himself up to be available, which is an incredible gesture," Martinez said.
"I need to assess him to see if he will be available for Everton.
"Ivan Ramis is not far away - if it is not Wednesday it will be Saturday (at Aston Villa) that he is available for the squad.
"James McCarthy is still a doubt. He played through the pain of the ankle injury he picked up at Norwich and we need to assess him and see how well he can cope with the amount of games we have in front of us."
Antolin Alcaraz (groin), Adrian Lopez (hamstring), Albert Crusat (knee), Ryo Miyaichi (ankle) and Ben Watson (broken leg) remain on the Latics' lengthy casualty list.