Substitute Ben Watson scored in injury time as the Latics won their first major trophy. Wigan were 9/1 just to win the game - which illustrates just how bigger outsiders they were.
Martinez said afterwards: "We were playing an incredible side. We didn't win by luck - from start to finish it was an incredible performance,"
"The FA Cup is such a special tournament, and everyone deserves to feel proud today."
He continued: "Everyone wrote us off before the game, but we were following a dream. You cannot describe the feeling at the moment. My players faced adversity and played with a smile. I am so proud of them."
"At half-time we were really down because we played well and when you are playing a top team, you need to take your chances. We were feeling maybe we wasted our opportunity."
The Latics played the final seven minutes against 10 men following Pablo Zabaleta's red card.
Former Wigan midfielder Martinez added: "These players don't know anything other than to keep fighting. At that time I was thinking about extra-time and how to use our man advantage. You could see the goal coming - the performance was magnificent, we deserved it.
Winger Callum McManaman was named man-of-the-match and Martinez said: "Actions speak louder than words, his display was outstanding like we see every day in training. He's a real diamond of English football. Today he's showed the world what he can do."
The Latics could become the first team to win the FA Cup and be relegated in the same season and Martinez said: "We've got two big games in front of us and we wanted to conserve energy, but it was difficult."
The Spaniard, when asked about he fact he has been strongly linked to the Everton manager's job, said: "Today is about today, the major trophy that Wigan Athletic have won."
They have another 'Cup Final' on Tuesday and nothing but a win will do if the likes of Sunderland, Newcastle and Norwich all win on sunday.