Penney has had a tough first season in charge, with a spate of injuries weakening the South Island side further after the departures of key players last year.
The Crusaders fell to a seventh loss in eight games last weekend, ambushed 37-15 by fellow strugglers Western Force in Perth, heaping further pressure on the former Munster boss.
In 2021, Penney was sacked five games into his second season as coach of the struggling New South Wales Waratahs.
Crusaders chief executive Colin Mansbridge, however, said cutting Penney mid-season might satisfy some fans but would not be a "very clever option".
"I don’t mind it from fans, because they are emotionally invested in it," he told Newstalk ZB.
"But from commentators, I think it's childish, frankly. When you see those things happen overseas, you don’t see improvements in results, that's the fact.
"There's a real opportunity to be thoughtful and logical, and just make sure to get the best out of the group and give them all the support you can."
Mansbridge said there was no "toxicity" or complete breakdown in trust between players and coaching staff that could justify striking early.
Penney has had to deal with less depth in key positions than his predecessor Scott Robertson, who delivered seven championship trophies in seven years for the Crusaders before departing last season.
"He’s probably had more to deal with there than even his predecessor - who definitely had injury worries to deal with," said Mansbridge.
"We’re all disappointed," he added.
"From front to back, side to side, the whole organisation is disappointed in the position we’re in and how we got here.
"What do you do though? You explore every element of the organisation (and ask) what can we be better at?"
The Crusaders host the fourth-placed Melbourne-based Rebels in Christchurch on Friday.
