"I do not think I have to especially explain why I make the decisions, but it is a permanent thing."
Wenger felt it had been an "interesting" few days for Arsenal, whose season is threatening to unravel.
He said: "When you do not win, nobody jumps off the roof, but the frustration does kick in.
"It is a good opportunity now for us to show we have strength and ability - you know how it works, you go from fantastic to a catastrophe, but real life is somewhere in between."
Wenger insisted: "So even if we are at the moment frustrated, it is not all doom and gloom. We have a strong belief in our ability and we have a good opportunity to show we care about the club and that we can qualify on Tuesday night."
The Frenchman rejected reports Gallas was set to be sold when the January transfer window opens in January.
"I cannot stop the suggestions, but for me he is a player who is committed to the club and can be stronger as a player because he took all of the problems of the team to his heart," said the Gunners boss.
"It can be a new start for him and he can be stronger for a player.
"But now I think we have to close this subject and you have to respect somewhere a little bit the privacy of the team."
The Arsenal manager added: "I believe the captain is the voice of the club towards the outside, and is one of the leaders of the team.
"However, I do not believe in just one man in the dressing room who sorts out all of the problems.
"A successful team is a shared leadership inside the dressing room. He (Fabregas) will be one of the leaders, but not the only one."