Howard was at fault for both goals in Sunday's 2-2 draw with Leicester City in the Premier League, gifting Nigel Pearson's strugglers a valuable point and continuing Everton's inconsistent campaign.
But Toffees manager Martinez has no plans to drop the USA international when the Merseyside club return to European action at Goodison Park.
"I think the goalkeeping situation is important," said the Spaniard. "Tim has come back from injury, he needs to play and get his match fitness.
"Tim is a very experienced footballer. To have 50 appearances in European competition we don't take lightly, and in moments like tomorrow we need that sort of experience."
Everton take a 4-1 lead into the second leg against Young Boys, but Martinez insists they will not be resting on their laurels.
"Complacency is a huge problem but we won't look at the game in any other manner to how we approached it last week," he added.
"We are concentrating on being ourselves and winning the football game and trying to look at the unique opportunity of getting into the last 16 of this prestigious competition.
"I feel we've got a strong squad in terms of numbers, we have got players back from injury, and we hope to get more back.
"We're very much trying to be as strong as we can be, we've got a really demanding week."