Kevin Keegan's City were dreadful and only after an almighty dressing room blast from the former England manager did they finally take the game to Spurs. Robbie Fowler gave them a chance of forcing extra-time when he took advantage of a howler of a clearance from Gary Doherty but Spurs booked their quarter-final place when Paul Konchesky's cross was turned in by substitute Freddie Kanoute.
It was a welcome return for Kanoute, back after a six-week lay-off with an ankle injury following a bad challenge by Leicester's Muzzy Izzet.
But Kanoute revealed Izzet had since apologised to him by leaving a message on his mobile phone.
Tottenham's top scorer said: "It has been a frustrating time for me but I just needed 15 minutes. My ankle was not very good last week but now it is healing well and I felt okay once it got warm.
"It has been tough because I was injured by a bad tackle but I've worked hard to come back as quickly as possible. Muzzy has since apologised. It was nice for him to do that. I have not got any bad feelings towards him now. It is in the past."
Kanoute's goal took his tally for the season to eight but he was more pleased to see Postiga get his first for the club.
Kanoute added: "I am very happy for him. It is always hard when you are a striker and don't score. We know what he can do on the training ground. This will give him the confidence he needs. I think he's been going through a little bit of a tough time but any striker goes through that when they are not scoring. He is young but it will hopefully be much easier for him now."
Acting manager David Pleat said: "When you go two goals up in a cup competition, you expect the opposition to throw the kitchen sink at you.
"We are not good enough to maintain the ascendancy for long periods but we looked dangerous on the break and some of our defending was terrific."
Keegan, however, was not so pleased. He declared: "I don't think I have ever been so angry as a manager as I was at half-time. We were not committed enough."