The Toffees managed to fight back from 2-1 down to grab a share of the spoils at Goodison Park on the back of their 4-1 win over Young Boys Bern in the Europa League on Thursday night.
In the wake of the result, Martinez spoke of his side's rapid drop in form but felt the players should be praised for fighting hard for the draw after the Foxes had hit back through David Nugent and Esteban Cambiasso following Steven Naismith's 57th-minute opener.
"It's one of those performances that comes on the back of playing in Europe," he told Sky Sports.
"We looked a little bit pedestrian but we knew it was going to be a difficult game. Scoring the first goal is always the hardest moment but once we did that we didn't control the play as we should have done. The two goals we gave away were quite soft for our standards."
He added: "The character we showed to get a point out of a game was a fantastic sign. It was very difficult when we were behind because Leicester had 10 bodies behind the ball.
"It's a great footballing compliment when teams come here and set up with many bodies behind the ball, but at times there is frustration breaking teams down and that shows through."
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