Martinez believes that Wigan's success in the cup will not have an adverse effect on their fight for Premier League survival.
He told ITV Sport: "The performance was absolutely brilliant with concentration throughout, to keep a clean sheet at Goodison Park speaks volumes.
"We deserve credit for handling the expectation of the crowd, we were a real threat going forward and stopped a dangerous Everton side going forward. My players deserve the credit for that.
"What we saw today is that players coming into the team makes us stronger. I guarantee that this cup run will not affect us in the league."
Wigan will slip back into the drop zone today despite not playing a league match, due to relegation rivals Reading and Aston Villa meeting at the Madejski Stadium.