Jan Vertonghen headed Spurs into an early lead, meeting Giovani Lo Celso’s free-kick in the 13th minute and nodding past Tim Krul.
Norwich equalised 12 minutes from time after a huge mistake from Vorm. The Spurs goalkeeper spilled a routine shot from distance and Josip Drmic bundled in from close range.
After a 1-1 draw over the 90 minutes, Mourinho’s men dominated extra time but couldn’t find a winner and the tie had to decided by a first penalty shootout at the new White Hart Lane stadium, which was won out by Norwich after Tim Krul proved more influential between the sticks than compatriot Vorm.
“I think we don’t deserve the result but that’s football,” Mourinho told the BBC after the match.
“As you can expect it was a difficult game, as I could expect some of my players were really really in trouble and they made an incredible effort to try.
“I am not going to say what everybody knows so this time I am not going to say that but I have to say Steven Bergwijn, it’s too much for him to play so many minutes like he is doing.
“I prefer to call Lucas [Moura] a hero, he is playing every minute of every game in every position to help the team but he told me he had to go out of he’s going to get injured.”
Erik Lamela sent his penalty over the bar, while Troy Parrott and Gedson Fernandes saw their penalties saved by shootout specialist Krul, who was famously brought off the bench specifically for penalties by Louis Van Gaal in the Netherlands World Cup quarter-final against Costa Rica in 2014.
Those saves proved decisive as Daniel Farke’s Canaries won out on penalties with three scored to Tottenham’s two.
“Harry Winks was completely dead,” Mourinho added.
“I think he’s started 11-12 games in a row, we had many many players in trouble.
“The solutions were solutions but we weren’t improving the team. We were the only team that could win in 90 minutes, we were the only team trying in the last 10 minutes.
“The same in extra time. Penalties are penalties, we missed them so congratulations to Norwich that’s the only thing I can say.
“I don’t have one single negative feeling towards my players, the opposite, they tried fantastic things. I am really, really sad for the boys, I can cope with the bad result and with negative moments, I’ve had so many, but I am really sad for the players.”
While extra time was playing out, the draw for the FA Cup quarter-finals pitted the winner with a home draw against either Manchester United or Derby County, who play tomorrow.
With Spurs exiting the competition, Mourinho has been denied another reunion with his former club.