Martinez had backed his veteran keeper before the game and hailed Everton's defensive resilience and the way Howard repaid his faith.
"Overall, we can take incredible satisfaction from this performance. To have that defensive ability, it was very pleasing," the manager said, quoted by the club's website (www.evertonfc.com).
"You rely on character and Tim Howard is an example of that. You get good and bad moments of form and there are always a bit more extreme views on a goalkeeper, whether you play well or make a couple of errors."
Howard has made 329 Premier League appearances for the club since joining in 2007, but supporters have made clear their dissatisfaction with his performances this season, eliciting angry reactions from the keeper.
However, there was no repeat of the ironic cheers that followed routine catches during league defeats by Leicester City and Stoke City, with Howard repelling Wednesday's third-placed hosts time and again.
"The way Tim prepares for the games, trains on a daily basis, faces adversity and takes responsibility is why as a manager you have blind belief in him," Martinez said.
"He is an incredible influence on the younger players and you will never see him blaming anyone else. He accepts responsibility."
Everton, who are 11th in the table, visit 14th-placed Chelsea on Saturday.
(Reporting by Simon Jennings in Bengaluru; Editing by David Goodman)
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