Fabregas limped out of the victory after just 14 minutes when he felt discomfort in his hamstring and was joined on the sidelines in the second half by team-mate
Fabregas said on Twitter last night: "I dont know if I'll make Sunday or not, but all I know is that from this moment to Sunday I won't sleep if it's necessary. I've waited too long to captain a final for Arsenal and I won't give up till the last second."
Wenger has admitted that he did not know how long the pair would be out for.
The worst case scenario for the Gunners is that Walcott and Fabregas, who has struggled with hamstring problems in the past, will not be fit for the second leg of the club's UEFA Champions League last-16 tie with Barcelona in two weeks.
Wenger said: "
"Fabregas has a hamstring problem. It is impossible to see how serious it is. We will know on Thursday."
Wenger confirmed that he will know by Friday whether
Manchester City captain Vincent Kompany has urged his team to take "one thing at a time" after lifting the League Cup trophy.