The Latics - currently 19th in the Barclays Premier League, three points from safety with nine games to play - have been in the relegation zone for most of the season and are being widely tipped to go down.
They face a tough-looking run of fixtures over the next few weeks, with Saturday's trip to Liverpool being followed by clashes with Stoke, Chelsea, Manchester United and Arsenal.
Martinez's men have suffered only one defeat in their last six matches, but also won just one of those and the sequence can be interpreted as a series of missed chances.
The Spanish manager has been frustrated by his side's failure to fully capitalise on their dominance in games, but is taking encouragement from the performances and has little time for doubters - something the club have continually had to put up with since their promotion to the Premier League in 2005.
Asked how he felt about people who might be writing Wigan off, Martinez - who guided the Latics to survival on the final day of last season - said: "I don't think it should surprise us at all - it is normal.
"As soon as we got promoted to the Premier League, people expected Wigan to get relegated and seven seasons later you will still get people who don't know the way we play or know the football club or how we are run behind the scenes.
"But that is our football challenge - to carry on defying the odds, playing our football and making sure we get the results we deserve.
"We are not here to please any pundits. We are here to keep improving as a football club and making sure we can be proud of our work at the end of the season.
"To do that, we need to get as many points as we can from the next 27."
Wigan captain Gary Caldwell is comfortable with the Latics' underdog status and is confident the team can upset the odds by winning the Liverpool match - as well as some of the other big games that come after.
"We've got a tough run of fixtures coming up which people will assume that Wigan Athletic can't possibly take points from," Caldwell told Latics Player.
"I think that's a good thing because we certainly believe we can win these games and to silence the doubters will give us a real platform to build on.
"Going to Anfield is always a difficult test, but if we play like we did last weekend (in the 1-1 draw with West Brom) and maybe get a little bit of luck then I'm sure we can go there and win.
"We'll have to be 100% though at the same time because they've got a lot of quality, especially in the final third.
"Luis Suarez is always a threat and Steven Gerrard is coming back into form as well now, but if we can get onto the ball and show the same attacking flair as in recent games then we can cause them lots of problems as well.
"We've got confidence at the moment, which isn't always the case for teams at the bottom of the table. We've not got any fear about facing opponents and we're playing attacking football which can only be a positive thing going into the final games of the season."