Spurs frustrated the Gunners for the majority of the first half but fell behind when Robin van Persie converted Bacari Sagna's cross and conceded again 11 seconds later after Cesc Fabregas had caught Wilson Palacios in possession.
Van Persie then added a third for Arsenal on the hour mark to cast doubt over Spurs' ability to finish in the top four.
Redknapp said: "The two quick goals we gave away turned the whole game upside down. I thought they were edgy, they were giving the ball away, the crowd was moaning at every mistake. I thought we were going to come in at half-time in great shape.
"There is no gap between the clubs in my opinion. I think two mistakes turned the game upside down."