United States international Howard failed to gather Jamie Vardy's low ball into the box, giving David Nugent the opportunity to initially pull Leicester level at Goodison Park after Steven Naismith had opened the scoring.
Howard then flapped at a Danny Simpson cross and was made to pay when Vardy pulled the ball back for Esteban Cambiasso to turn home.
Matthew Upson's late own goal ensured Everton salvaged a point, but the Merseyside club are without a home win in the top flight since December and sit 12th in the table.
There have been calls for Joel Robles to be restored to the starting line-up at the expense of Howard, but Martinez is standing by the former Manchester United keeper.
The Everton manager said: "I don't see Tim as directly responsible for the draw.
"The first one is quite an unlucky action. He gets in some sort of a block, it hits John Stones' legs and it ends up in the Leicester striker's footpath.
"We have three players around him and it ends up with him [Nugent]. I don't think it was such a major error.
"I don't think it would solve anything if we just single out the player who made that mistake. As a team we need to defend much better in those situations.
"Tim Howard is one of our leaders, one of the most solid performers. What he brings as a goalkeeper is his understanding with other players, what he has achieved in the game, and when he is fully fit, he is a very strong performer.
"His performance against Chelsea was outstanding and his performance against Young Boys, after the first goal when he doesn't see the ball, was terrific.
"I don't think that is the difference between getting three points and one point [against Leicester]."
