Lambert received a mixed welcome as he walked out at Carrow Road, with a few jeers heard among general applause for the man who masterminded the Norfolk club's rise to the top flight from the depths of League One.
However, the former Canaries boss, who is in dispute with his old employers after an acrimonious departure during the summer, enjoyed the last laugh as substitute Andreas Weimann hit a second-half brace to turn the tie around after Brett 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.
Villa's travelling support were in full voice on a bitterly cold night in East Anglia and Lambert hopes to give them more to cheer about over the coming months as he aims to reconstruct the midlands club.
"I have never been to Wembley, although I have been to watch a game," he said.
"But it's not anything I have thought about, we have still got a couple of games to go.
"However, it gives the club something to look forward to. The fans deserve a pick-up as well.
"Whatever happens [for the semi-finals], Villa Park will be jam-packed.
"I will be more pleased with the pleasure the players get from it because I don't play the game any more."
Lambert remained humble despite what in the end was a comfortable victory over Chris Hughton's men on his old stomping ground.
"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," said Lambert, who is been represented by the League Managers' Association in his arbitration hearing with Norwich, which is set for early next year.
"You like to think they [the 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' team now, he has done fantastically well with the position he has got them into and we will try and catch them."
Lambert 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 heading into last night's game, 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, who turned 54 yesterday, said: "We needed to make sure we held on to 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."