The Frenchman told Sky Sports: "It's a recurrence of his hamstring. We knew before the game it was not perfect.
"We will see if we have long regrets or short regrets. I don't believe it's too bad, he doesn't think it's too bad."
Wenger is hoping the injury is not too serious, with a scar on the injured tissue the best prognosis rather than a new pull to the hamstring.
He said: "If it's a pull again it's three weeks (out) so we hope it is only a scar."
Wenger admitted he could not say whether the Gunners would have won without Fabregas.
"That's very difficult to predict. I believe we were dominant. I believe in the last 20 minutes we could have made the difference (to win the game)."
Wenger revealed he was considering signing a striker in the January transfer window because of Robin van Persie's ankle injury.
He said: "We are in the market with our eyes open. We are a bit short as we planned to play with Robin the whole season."