Victory for Martinez's men would have handed city rivals Liverpool the initiative in the title race, leading to suggestions of mixed emotions in the Goodison Park stands on Saturday.
There was little evidence of this when the ground erupted to acclaim Ross Barkley's sensational opening goal and, although leaders City took charge through Sergio Aguero and an Edin Dzeko brace, Romelu Lukaku's 65th-minute header set up a breathless finale.
Defeat ended Everton's hopes of UEFA Champions League qualification, but Martinez was pleased to end a memorable home campaign with his team's fighting qualities on full display.
"I think everyone that watched the game understood straight away that if anyone questioned our integrity - not just as a football team but as a football club - they had not reason to do it," he said.
"The effort, the character of the players, the intention of winning the game was clear for everyone to see from the first second until the last.
"The way we celebrated Ross Barkley's goal is as big a roar as you got at Goodison for the whole season.
"So I'm proud of the football club that we were very much a team wanting to win.
"I think it's clear that we tried absolutely everything to beat this Man City side."
Aguero's goal was his 17th in the Premier League this term and the mercurial Argentine's injury curse struck again in the act of scoring.
He hobbled out of the action to be replaced by midfielder Fernandinho and, paradoxically, Martinez felt City's loss of their talisman had a greater impact on his own side as Yaya Toure was pushed into an advanced role to influence proceedings.
"I do think that the injury to Sergio Aguero affected us more than it affected them," he explained.
"In many ways it was a fascinating tactical games and we tried absolutely everything.
"In the last 20 minutes we gave a proper, proper go. We showed an incredible bravery in everything we tried to do from the first second to the last.
"We tried to win a football game and I think it's fair to say that we didn't deserve to lose the game."
