However, Spurs gave away two sloppy goals before the half time interval to give themselves an uphill struggle in the second period.
"The two sloppy goals we gave away turned the game upside down," Redknapp said after the game.
"I thought Arsenal were edgy and giving the ball away.
"The crowd was moaning at every mistake. I thought we would come in at half-time in great shape.
"For 42 minutes I didn't see anything where I was sitting thinking, 'we are out of our depth here'.
"There is no gap between the clubs in my opinion.
"We made two mistakes. They let in four goals at Manchester City (last month), does that make them a bad team? That's how it goes."