The defender sprained his ankle as his side went down in Greece, but the result mattered not as the Gunners still finished top of Group F having already qualified.
“Santos suffered a bad ankle injury. It looks like he will be out for a while. We have [Kieran] Gibbs coming back in two to three weeks," he told reporters.
“Hopefully Santos will not be too long but, for Saturday against Everton, he looks to be struggling."
The Frenchman fielded a side made up of youth and fringe players and this move came undone as a handful of defensive mishaps handed victory to the hosts, who missed out on qualification thanks to Marseille's late win at Dortmund.
Wenger told Sky Sports News: “I never like to lose and I have some regrets. We must give credit to Olympiakos tonight because they played a very physical game.
“In the first half it was very difficult for us and I don’t think we had the right tactical approach, we played too many short balls.
“We were unlucky to lose [Lukasz] Fabianski and then in the second half at 2-1 it looked like we were going to come back but they were always dangerous and in the end they deserved it.”
"[There was a lack of communication] Particularly in the defence many times, they looked at each other.
“Those players haven’t played a lot together. Many of them have no experience in the Champions League as well so [they were] a bit surprised by the pace of the game.”
The injury picked up by Fabianski forced Wenger to bring on Victor Mannone who struggled in goal, no more so than in the build up to the second goal from David Fuster.
“I felt tonight we didn’t help our goalkeepers because when we could have given them easy passes we didn’t,” Wenger added.
“We exposed them with our lack of quality in the passes we gave them and they were quite brave. Of course it was not the best of starts when you come on and concede a goal like we did.“Unfortunately in Europe if you are not at 100% at the start of the game it is very difficult to win and tonight Olympiakos had a good chance to qualify and were 100% up for it.
“We had the early chances in the game and we didn’t score. Physically I think they gave absolutely everything.”