Arsenal are now unbeaten in 20 league games against Spurs who went into the match in fourth place, level on points with the home side and hoping for a performance that would show they could mount a sustained challenge to finish in the top four this season.
A first-half devoid of meaningful goalmouth action appeared to be heading for stalemate until Arsenal stunned Spurs just before the break with quickfire goals from Robin van Persie and Cesc Fabregas.
"The two sloppy goals we gave away turned the game upside down," Redknapp told a news conference.
"I thought they (Arsenal) were edgy, giving the ball away, the crowd was moaning at every mistake. I thought we would come in at halftime in great shape.
"For 42 minutes I didn't see anything where I was sitting thinking 'we are out of our depth here'," added Redknapp.
Asked if the defeat indicated a gap between the two teams, Redknapp replied: "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."
Arsenal have torn teams apart at the Emirates this season and have now scored 20 goals in five league matches on home turf.
"We lacked fluency in the first half hour, we played a little bit with a handbrake on," manager Arsene Wenger said.
"But we took advantage of the first goal, then straight away of the shock caused by the first goal and second half we always played a bit restricted. But once the third goal was in you did not have the impression Spurs could come back."
CHAMPIONS LEAGUE
It was their defensive solidity against Spurs that pleased Wenger the most after his side threw away a 2-0 lead at West Ham United last weekend and also conceded a last-minute equaliser in the Champions League against AZ Alkmaar in the preceding game.
"It was important for the team not to concede today. Any goal after what happened recently could have caused a panic," said the Frenchman.
"Despite the fact we won 3-0 we had a good defensive performance. Our back five were very efficient, we dealt well with their offensive players. At the end of the day we did not give any goal chances away."
Manuel Almunia was recalled ahead of Italian Vito Mannone and the Spanish keeper enjoyed a quiet return.
Almunia began the season as first choice but had not played since conceding four goals against Manchester City on Sept. 12, firstly sidelined by a virus and then out of favour as Mannone was handed his chance.
Wenger drew laughs when he said the raucous Arsenal fans among the 60,000 capacity crowd made so much noise he could not communicate with his players, forcing him to throw his jacket to the ground in frustration in the second half despite his side coasting to victory.
"I was frustrated, I could not communicate with the players because of the noise of the stadium, I'm not used to that," Wenge
