Howard was one of the stars of the World Cup last year, but his form has dipped considerably since he returned to England.
The American was dropped for Joel Robles at the turn of the year after making a number of mistakes and he was at fault again at Goodison Park on Sunday as Everton grabbed a lucky point thanks to an 88th-minute equaliser.
Just after Steven Naismith had put Everton ahead, Howard pushed Jamie Vardy's shot into the path of David Nugent to allow the Foxes to equalise and soon after the goalkeeper flapped at a cross, and Esteban Cambiasso drove a low shot into the home goal.
Luckily for Howard and Everton, Romelu Lukaku's late diving header flew in after a huge deflection off Matthew Upson to snatch a point for the hosts.
"I don't see Tim as directly responsible of the draw," Everton boss Martinez said.
"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.
"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."
Everton won only once during the eight-game stretch Robles had in goal, and it appears the Spaniard will not replace Howard in goal for Thursday's Europa League game against Young Boys.
"Tim Howard is one of our leaders, one of the most solid performers," Martinez said.
"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 today."
Howard was not the only one who failed to perform on Sunday.
Ross Barkley lacked dynamism and creativity, Aaron Lennon quickly faded after a bright start and Lukaku missed several opportunities before helping the hosts earn a point with his deflected header.
Everton's home form was key to their fifth-place finish last term, but they have won three and drawn six at Goodison Park this year.
Nigel Pearson was disappointed not to take three points back to Leicester.
"The dressing room is very disappointed because we did very well today," the Foxes boss said.
"We have got to turn these sort of performances into wins
There is not getting away from the predicament we find ourselves in but the performance was there today
We will have to bounce back."
Leicester are four points from safety and have Manchester City, Tottenham, Southampton and Chelsea to face in their final 11 games.
Pearson has not seen his team win in their last five Premier League matches, but he is still confident they will stay up.
"If we apply ourselves in the way we did today and at Arsenal, I think we will be fine," he said.
"The target is for us to get out of the mess we are in
I can't predict what (our) points total is going to be
First and foremost we have to stay in touch.
"We have been bottom since late November
It is a long time for the players to deal with the pressure of being in that situation.
"They conduct themselves exceptionally well
The spirit they have showed in a difficult season is very commendable."
Source : PA
Source: PA