The Latics face Arsenal tonight with the odds firmly stacked against them.
However, Martinez believes that recent victories over Liverpool and Manchester United, as well as a positive performance at Chelsea, shows that his players can compete with anyone.
"We are capable of getting results against anyone," Martinez told reporters. "We proved that against Manchester United but also against Chelsea and Liverpool. Those games allowed us to break a mental barrier that we had in the past.
"We went to Anfield and won, and in my eyes we beat Chelsea, even if we didn't win the game.
"When we are at our best, and we have to be perfect, we are a competitive side no matter who the opposition is."
Victory for Wigan would lift them five points clear of the relegation zone.