Lambert received a mixed welcome as he walked out at Carrow Road, but the former Canaries boss, who is in dispute with his old employers after an acrimonious departure during the summer, saw substitute Andreas Weimann hit a second-half brace to turn the tie around after Brent Holman had cancelled out Steve Morison's opener.
Christian Benteke cracked in a fourth during stoppage time to move Villa within 180 minutes of Wembley. Lambert said: "I thought we were excellent for the whole game. We have been playing like that since the Sunderland game, but I am delighted, I really am."
Lambert, who is being represented by the League Managers' Association in his arbitration hearing with Norwich, which is set for early next year, maintained he will always look back on his time at Carrow Road with pride.
"I had three great years here. We gave anyone a really good run for their money. I love the club. I've got nothing but praise for the football club," he said. "You like to think they [fans] appreciate what you have done and I appreciate the support they gave us.
"It is great club with great fans, but this is Chris' (Hughton) team now, he has done fantastically well with the position he has got them into and we will try and catch them."
Lambert had handed Darren Bent a rare start, only for the England striker, who saw an early one-on-one saved, to limp off just after the hour with a hamstring problem. Lambert said: "I thought he looked pretty sharp. It was a blow for us, I don't know how serious it is."
Norwich had been defending an unbeaten 10-game run and certainly had their chances to put the tie beyond Villa at the start of the second half, when Morison missed twice in quick succession and Villa keeper Shay Given produced a brilliant reaction save to deny Grant Holt.
Canaries boss Hughton said: "We needed to make sure we held onto our 1-0 lead longer, and then at the start of the second half, we had a great chance and if that goes in then possibly it is a different story.
"Villa are a good footballing side and they were more clinical than us. It is really disappointing because we had been on a good run. We have to take it on the chin and now need to make sure we can get back on track for Saturday against Wigan."
- Sports & Recreation
- Steve Morison