Norwich looked comfortable defending their 2-1 lead until the third minute of added time when they failed to deal with a free-kick and Dan Harding lashed home the loose ball to take the tie to extra time.
"Our fans were probably walking out at that stage thinking the game was over but it turned out to be a good night in the end," said Pardew after his side won the shoot-out 6-5.
"That was probably the worst we have played for some time but we hang in there, we don't want to give in and that showed even in the penalty shoot-out.
"Papa took his goal very well but we were found wanting at times, there were some strange decisions and the referee had a funny game. But it's nice to win when you don't play well and I think it shows our never-say-die spirit."