The North Londoners have taken just four points out of a possible 15 so far in the Premier League and conceded two own goals in a 4-3 defeat at Blackburn Rovers on Saturday.
Wenger, who marks 15 years as manager next month, is enduring one of the worst sequences of his career in England, with Arsenal 17th in the league and just a point above bottom club West Bromwich Albion.
Speaking at a Sport Industry breakfast meeting, Gazidis made a strong defence of the Frenchman.
"Arsene Wenger is not broken. To see him portrayed as an idiot is damaging, not to him or the club but to the game," he told the BBC.
"[Sacking him] is a route we are not going to go down. He didn't suddenly become a bad manager or out of touch. That's nonsense."
Despite encouraging performances in the Champions League, Arsenal have conceded 14 goals in five Premier League games, with 12 of them in their last two away matches. They also have the worst goal difference (-8) of the 20 top-flight clubs.
Gazidis said the club had a long-term strategy and would stick with it.
"If we get into short-termism we will do more damage to the club. He [Wenger] is frustrated but very, very focused on putting things right and is as positively engaged as ever to drive the club forward," he added.
"The club is not in crisis. There's no division in the club. We work together.
"The club is focused on a responsible, sustainable model," said the chief executive. "Football's going that way and people are trying to get where we already are. We represent the future of football.
"We will be unmoved in the way we do things and will not be swayed by talk of a crisis."
Wenger strengthened his squad late in the last transfer window, bringing in defenders Andre Santos and Per Mertesacker, who both played on Saturday, but the back four have yet to gel.
Alex Song and Laurent Koscielny were responsible for Arsenal's own goals against Blackburn.
"Our season depends now on how well we respond to this disappointment and how quickly we can cut out the mistakes we made on Saturday by giving away goals that we should never give away," Wenger told the club website.
Wenger detected a "lack of concentration, a lack of communication, a lack of coordination and individual urgency" in some of his players.
Arsenal are expected to field a mixture of first-team players and youngsters in their League Cup third round match against fourth division Shrewsbury Town later on Tuesday.
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