With question marks being raised over the partnership between Gallas and Kolo Toure, the Arsenal boss knows he needs to strengthen his defence during the summer and will delay a decision over his club skipper for next season.
Wenger said: "I cannot answer that question at the moment. I want to analyse the season after the season. At the moment he will be my captain until the end of the season.
"I made that decision and I have to stand up for that decision. I have to protect the team and the individuals as well at the moment."
Former Arsenal defender Lee Dixon slammed Gallas for his poor defensive display at Old Trafford last week and also questioned his ability to captain a young Arsenal side.
Wenger admits this has been the lowest week of his managerial career, but he was not prepared to single out Gallas for their failure to win a major trophy this season.
Wenger added: "We were leading at Chelsea, Liverpool and Man United plus we were leading at home against Liverpool. We can score goals. What we could not stop is conceding goals in big games.
"When you know that nine times out of ten, the team that wins the big games is the team who scores first. We lost these games after being in front. We suffered more as a team defensively rather than offensively.
"They get criticised and maybe we deserve critics at the moment but overall the team has made good progress this year. The most important thing is we finish well now.
"I believe he (Gallas) has learned a lot this year and I can only say that his commitment and desire to do well was exceptional. For the rest, I wouldn't like to go into any individual assessment at the moment.
"It is lowest week I have had here. We were so close to qualifying in the Champions League and if we had won at Manchester United we would have had a very strong chance to win the title.
"It's been a year of hard work - probably the hardest we have ever worked here. So to lose everything in four or five days is very hard to take."