The Gunners raced into an early two-goal lead before an Alex Kacaniklic strike and a Dimitar Berbatov double turned the game in the visitors' favour.
The hosts managed to get back into the game through Olivier Giroud's second goal but were denied a win when Mikel Arteta's last-minute penalty was saved.
When asked if his side deserved to win the game, Wenger told Sky Sports: "It’s difficult to measure. We had the possibility to win the game but we didn't take it.
"We were 2-0 up and gave two cheap goals away, but after that we have shown a fantastic spirit. I believe we have not shown enough urgency in our defending at 2-0 up."
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|25/1||Olivier Giroud is 25/1 to finish as the Premier League's top scorer with Paddy Power|
He continued: "In the second half we have done great, and we were maybe a bit unlucky in missing a penalty.
"We had plenty of chances, even at 3-2. I felt the team continues to fight and will not give up. The spirit was absolutely fantastic on both sides. It was a good football game.
"But you want this little plus that you can get - the edge - going for you. That didn't happen today, but it has been a good game."
After admitting that the handball which saw his side awarded a late penalty was probably not deliberate, Wenger hailed the performance of two-goal striker Giroud.
He added: "He showed us that he grows from game to game and becomes more and more dangerous - that he is an Arsenal player."