"The fans were absolutely fantastic in Milan and we can only say sorry," the Frenchman told reporters on the eve of the FA Cup Fifth Round visit to Sunderland.
"Tomorrow there will be another fight and we want them to be on our side. I am sure they will be," added Wenger.
"Defeat never gets out of your system because you take it with you until the last day of your life. But when you love competition you always strive for the next one and prove that you are ready for a new fight."
Arsenal may be reeling after suffering their worst defeat in European competition on Wednesday but Wenger said he now wanted to see a reaction from everyone in the camp.
"You can find 100 explanations for the fact we had a poor performance and an off day," he said.
"I believe for us, for the rest of the season, it is important not to dwell on that too much, focus on the next performance, respond in a positive way and ensure we have the mental qualities to be at this club.
"We have to ensure straight away we are capable of responding, that is the real test."
Wenger's Arsenal have gone seven years without winning a trophy and the FA Cup takes on even more significance with the North London club fourth in the Premier League, 17 points behind leaders Manchester City.
"It was always important," said Wenger, referring to the world's oldest cup competition. "But because we had a big disappointment in the last game it becomes more important.
"We have an opportunity to qualify for the quarter-finals. It is important we are up for that and do not feel sorry for ourselves because of that performance in Milan."
Arsenal will be without injured defenders Per Mertesacker and Laurent Koscielny for their second visit to Sunderland in eight days, having won 2-1 there in the Premier League last weekend.
Forward Gervinho is ready to return after his Ivory Coast team were beaten on penalties by Zambia in Sunday's Africa Cup of Nations final.
