Former Blues defender Gallas has come in for criticism following his reaction to the last-gasp draw at Birmingham when he broke down in the centre-circle, as well as a controversial magazine article commenting on Theo Walcott's development.
Following the loss to Chelsea, the veteran French centre-back went over to the travelling support and threw his shirt into the crowd, which he insists was nothing unusual or any kind of statement.
Wenger, though, maintains the 30-year-old is the right man to lead his young Gunners forward.
"You have the same William Gallas - and the same people said it was a good choice to make him captain when we were five points ahead, and you have not to go too much overboard."
Wenger maintained he had no problem with his captain's comments concerning Walcott.
The Arsenal boss said: "He said Walcott could be the next Wayne Rooney, but he has to work. What is wrong with that? You want at 18 years of age to not work? It's unbelievable.
"I read it really carefully, it didn't say anything wrong on that. After the way it has been turned, yes.
"If you want to win the World Cup you have to accept that your players are highly exposed, you have to accept that you have to work.
"Is it an insult to say somebody has to work? I don't know, I don't think so."
Wenger believes Gallas is an easy target during what has been Arsenal's worst run of form in nine seasons.
He said: "I believe at the moment when you don't go well, everybody is analysed a little bit more, with scrutiny.
"But what we want to do is perform well as a team again and we know we can do that.
"And on Sunday, for example, we played okay, but we have to improve. Recently what punished us a lot is that defensively we have made big mistakes."
Wenger insisted: "William has my full support and my full backing and I am completely behind him, and behind the team as well.
"We are going through a bad patch, I agree with you, but we want to come back and win the games again that we can win."
