The Latics, who are battling for their Premier League lives, defied the odds at Wembley Stadium on Saturday to collect a 1-0 win.
Ben Watson nodded home the only goal of the game in stoppage-time to hand Wigan victory in their first final appearance and earn them major silverware.
Martinez, who has spent four incident-packed years at the Latics helm, was quick to pay tribute to the collective effort put in by everyone connected with the club as they toasted a remarkable success.
He told Sky Sports: "Immense pride. It's winning one of the most significant trophies in world football.
"You can imagine to do that with our fans, with what we have been through, it's an incredible achievement. It's one of them moments that shows the example of the FA Cup - follow the dream and achieve it. And on top of that there is the performance, we were well worthy winners. It's an incredible statement when you play against Manchester City.
"I think it's fair to say a couple of weeks back we played another game against Manchester City and it was a similar performance, but we couldn't score a goal.
"Today in the first half it felt like we have had the chances and haven't taken them. It was an incredible show of character in the second half to replicate that. We stopped Manchester City in the second half and after the sending off, the game was coming into our hands. I thought it was a reflection of the whole game how we won.
"We need to hold any celebrations for now because staying in the Premier League now is our league title."
Martinez has seen his future at Wigan called into question of late, with it suggested that he is a leading candidate to succeed Manchester United-bound David Moyes at Everton.
The Spaniard is, however, keen to steer clear of such talk for now.
Preferring to keep the focus locked on a collective effort, he said: "It's just a feeling of pride. The performance today wasn't off the cuff or an accident, I thought it was the work of the last 10 months of the players.
"That gives me a great sense of pride and gives me belief. I believed that if we kept working hard on a daily basis, the rewards come along the way. I think that was an example today.
"I am extremely proud of this group of players that they showed how to be brave, how to believe and how to play football in a manner that can get you trophies."