Wenger is spurred on by derby win
Teenager Henri Lansbury, one of eight changes by Wenger, who was serving a one-match touchline ban, swept the visitors ahead from close range on 15 minutes.
Robbie Keane, who came on at half-time, scored an equaliser three minutes after the restart to level for a much-changed Spurs side, which saw Brazilian midfielder Sandro make his debut.
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Hide AdHowever, neither team could find a winner in normal time, but Samir Nasri's penalty double and Andrey Arshavin's goal sent the Gunners through in extra time."
Wenger had named a strong side with the likes of Arshavin and Marouane Chamakh on the bench.
"We have got a few reproaches that we did not take the competition seriously, it was a derby and to go out straight away for us would be difficult," said the Gunners boss. "If everybody is fit, I can go as well for this competition. The big competitions are the Champions League and the (Premier League] championship. But I want to win every single game I play."