Redknapp felt his players' response to Sunday's Wembley defeat by Portsmouth proved their character.
Spurs beat their north London rivals for the first time in the Premier League in 11 years with a wonder-strike from Danny Rose and second-half goal by Gareth Bale sealing the outcome.
Spurs are now right back in the race for the final Champions League spot, trailing fourth place Manchester City by one point.
"It was a real London derby, very competitive and played in a good spirit," said Redknapp.
"We worked very hard and lifted ourselves after a difficult day on Sunday. To come out and turn in a performance like that was great.
"Arsenal were the perfect game for us to play, the crowd were passionate and got behind us.
"We knew the importance of the game and that if we won we still have a big chance of fourth. The players responded with a fabulous performance.
"We're still in there for fourth but it's going to be hard."
Redknapp praised Rose's wonder-strike with the 19-year-old, making his league debut, viciously volleying Manuel Almunia's punched clearance home.
"It was an amazing goal from Danny. He's a left sided player but I played him on the right because I thought he'd give us a bit of energy," he said.
"That was a wonderful strike and we'll never forget that."