The Latics caused a significant upset on Wednesday with their 1-0 victory against Barclays Premier League leaders United, who went into the contest off the back of an eight-match top-flight winning streak and had triumphed in all 14 of the previous meetings between the two clubs.
Martinez spoke of his team achieving "mission impossible" when looking back on that game.
Yet he feels the forthcoming fixture against third-placed Arsenal - winners in nine of their last 10 league matches and their past seven at home in all competitions - is a more tricky proposition.
"Probably this is an even tougher task," Martinez said.
"We are going away from home and playing against a side who have been as successful as ever at home.
"If you look at the last few performances they have been untouchable in the way they are playing their football, controlling games and scoring goals.
"But we know that if we are at our best, we can be competitive against anyone."
Wigan have been on a fine run themselves, with the United result, which moved them out of the relegation zone for the first time since October, meaning they have taken 16 points from their past 10 games.
In the last two of those, they have been the subject of some hotly-debated decisions by match officials.
Martinez received an apology from referees' chief Mike Riley following the Latics' 2-1 defeat at Chelsea on Saturday, in which Branislav Ivanovic and Juan Mata both struck for the hosts from apparently offside positions.
Then on Wednesday, Wigan were denied a seemingly legitimate goal against United before opening the scoring with a strike that came from a corner which replays showed should not have been awarded, and later escaped punishment when their defender Maynor Figueroa appeared to handle in the area.
Martinez had been strong in his criticism of officials following the Chelsea match.
But after the events of midweek he offered them a show of support, suggesting that while referees are in need of all the help - such as video technology - that can be provided to them, they are of a higher standard in England than elsewhere in Europe.
"All clubs get bad calls, that is the nature of the game," Martinez said.
"On Wednesday, we had what I thought was a bad call against us, but then we got a bit of fortune in another call and that levelled it up a little bit.
"You might expect that in games, and against Chelsea, I want to believe that was a one-off situation - where you get several very important calls go against you.
"That is a very unfair situation from which to try to get a positive result, even when your performance deserves that.
"I think referees need all the support we can give them, but I have said before - I think the referees in our league are of a better standard than in France, Spain and Italy.
"We need to keep on helping the level."