The Spaniard praised his team's performance in the comeback victory over West Brom, although Jean Beausejour has been ruled out of the FA Cup final after damaging his hamstring
Callum McManaman's later winner handed the Latics a crucial three points at the Hawthorns, with earlier goals from Arouna Kone and James McArthur cancelling out efforts from Shane Long and Gareth McAuley.
The result puts Wigan two points adrift of safety - with a game in hand on their relegation rivals against Swansea on Tuesday - and Martinez has now backed his squad to survive the drop and beat Manchester City in the Wembley showpiece.
"It was a performance full of character," Martínez added. "I couldn't be prouder of the players. I don't think many teams score three goals from open play against West Brom," he told reporters.
"Every other club fear to lose something; we don't. We don't fight to avoid relegation. It is not a negative, it is a positive. As a football club, we win the title every time we stay in the league. We have got a big-club mentality in those players.
"We are ready to win both trophies, the league and the FA Cup. We don't hope to get out. We know how to get out of the situation. Our players have the experience so that they are not going to get affected by the occasion."
It was not all positive for Martinez, though, with wing-back Jean Beausejour being ruled out of contention for next Saturday's FA Cup final with a hamstring injury.
"Jean is the negative, he pulled his hamstring and it doesn't look great," he continued.
"These sort of injuries are usually 10 days."