Leicester celebrated their title in style on Saturday, as Jamie Vardy's double and an Andy King goal put Claudio Ranieri's team firmly in command at the King Power Stadium, before Kevin Mirallas snatched a consolation late on.
The rampant hosts could easily have scored more than three, though, had Vardy converted his second penalty of the game. Meanwhile, Everton goalkeeper Joel Robles made several good saves.
And Martinez was left downcast after the match.
"I don't think there were any positives to take from today. Not at all," the Spaniard said.
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"While this is a day for Leicester City and to celebrate them - they have achieved an incredible feat in winning the Premier League and deservedly so - from our point of view it was very disappointing.
"We never turned up and we never understood what was needed. I think we thought we were part of a celebration and that it was a footballing occasion that you could just concentrate about what we were doing on the ball.
"We looked like a group of individuals and I thought, off the ball, we didn't have any intensity or concentration and when you do that against any team you'll get punished, but especially against Leicester, who have won the league on the basis of being very intense.
"In any team you have to have aspects that will allow you to grow in a performance and get a win. We had that last week against Bournemouth and this week we looked like a different side."