Howard has kept only four clean sheets in his 20 appearances for Everton this season, albeit not helped by a porous defence, and has been criticised for not commanding his six-yard area.
Yet Martinez remains a staunch supporter, saying Howard's value to the team is being overlooked by fans.
"He had mistakes but he had big moments. His day-to-day work shows me the strength, power and positive effect he has on young players," Martinez told British media.
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"I feel we are a stronger team with Tim Howard in the dressing room."
Everton's reserve goalkeeper Joel Robles, signed in 2013, has not managed to dislodge Howard as first-choice, with all his appearances this season coming in the club's run to the League Cup semi-finals and the FA Cup.
They also have several young keepers, including Czech Jindrich Stanek who is yet to make a first-team appearance.
Despite his backing of Howard, Martinez is keeping an open mind on his goalkeeping options.
"Whatever happens at the end of the season you cannot guess it now and it would be wrong to try to guess that," Martinez said.
Everton, who are 11th in the Premier League after 20 games, face third-placed Manchester City later on Wednesday.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Martyn Herman)
