Arsenal fell seven points behind its North London rivals after Gareth Bale and Aaron Lennon inflicted defeat on Wenger's team on Sunday with goals just moments apart.
"It's very frustrating," Wenger told Sky Sports. "But we have to put the energy in like we did today and keep going. You never know.
"It would be absolutely terrible not to continue to fight like mad, because there were a lot of positives in the game.
"What happened today was repeated so many times in the big games. It's difficult being 2-0 down - in any big game you have a big task."
Bale and Lennon were both allowed to run behind the Arsenal back line and advance on Wojciech Szczesny as they grabbed quickfire goals, and Wenger admitted that his side's defending did not look good on first glance.
"I will have to watch [the defending] again, but it looks a bit like that," Wenger conceded when asked if their poor defensive display had proved costly. "It's difficult to swallow a defeat like that because of the effort we put in and because the energy levels we produced for the 90 minutes was tremendous.
"But we made it difficult for ourselves in the first half. We had no shots on goal, we were 2-0 down.
"In the second half we came back and dominated the game but there were many fouls that intelligently stopped the game and it was difficult to get a flow in the final 20 minutes.
"The game suffered from too many stops in play and we didn't find the second goal."
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