Niko Kranjcar and Jermain Defoe fired the goals to help Tottenham gain a 3-0 win against big-spending City at White Hart Lane on Wednesday night.
"That was as good as we've played over the 90 minutes," Redknapp said after the match.
"We never let off. All the chances were created by us, it was a great performance by us.
"They all worked well, the whole team defended well, every one of them. We were strong. It was a great performance.
"They're a strong side, I honestly believe in the next four or five years I could see them going on to win the championship because of the backing they've got. I think they'll get stronger and stronger with Mark Hughes.
"But we were the better team tonight, no doubt about it. We thoroughly deserved our win."