The Canaries manager was hesitant when asked if he saw himself at the club next season, while Aston Villa boss Alex McLeish vowed to win over supporters after a torrid campaign
Lambert hailed his players for their efforts over the course of the season after goals from Grant Holt, who was later named the club's player of the season, and Simeon Jackson secured a comfortable last day victory.
However, when asked if he saw himself at the club at the start of next season, Lambert paused before replying: "It's a hard one to answer. I've got a contract here. I'll see what happens and think about what we've achieved."
Norwich's win ramped up the pressure on under-fire Aston Villa manager Alex McLeish but Lambert said he would not concern himself with speculation regarding a move to another Premier League club.
"I don't worry about myself to be honest, I just worry about the team," Lambert said. "Speculation like that doesn't bother me, I just get on with it. I don't know, we'll have to wait and see."
Lambert admitted that his team had exceeded all of the targets he had set at the beginning of the season, when the Scot had been concerned solely with keeping the Canaries in the Premier League.
"I thought we carried on from last week," Lambert opined. "We were terrific all game and deserved to win. It was a fitting way to end an incredible season.
"The target was always to stay in the league. We surpassed that long ago. It's been unbelievable, what's happened here – it's never easy to get one year of success but we've had three.
"They've exceeded my targets by miles. It speaks volumes to their character."
McLeish, meanwhile, admitted that Villa's performance on Sunday and season as a whole had been disappointing but vowed to win over the club's supporters.
The former Birmingham City manager pointed out that the Villa squad had been decimated by injuries and claimed he had had to "pull out all of the stops" to keep the club in the top flight.
"It was an extremely flat performance," McLeish admitted. "Norwich were sprightly and sharp and we were the opposite.
"Arguably some of the teams that have been relegated were stronger than us in terms of their overall squad. But that was an unacceptable performance.
"It's been a hell of a challenge. I've done my utmost, I've tried to think left-field when we needed results. In the end we got over the line.
"It was a big test for me as a manager. People will not see it as a glorious season but I had to pull out all of the stops. It's been as tough as it's ever been.
"I can totally understand the fans' frustration. I carry the can for their performances. Unfortunately I don't tell players to misplace a ten yard pass. I have to turn the opinion around. I'll do my best."
McLeish is keen to make changes and strengthen the Villa squad over the summer but is not expecting to receive a large transfer kitty from owner Randy Lerner, who he will meet next week.
He insisted that he had never feared for his job during his time at the club, despite the pressure which he has come under during the season.
"The chairman has made it clear that he won't put millions of pounds in to bring giant names to the club," McLeish said.
"We've still got to wheel and deal a bit. But we have to make some change because two seasons like this in a row isn't acceptable for Aston Villa.
"I've not had the riches to spend that other managers enjoy, but I believe I can turn Aston Villa around by changing things and bringing in quality players that will work their socks off.
"The emergence of some of the young players was positive. They've been thrust in, a few ahead of their time, but that will stand them in good stead in terms of their confidence.
"You can't start fearing for your job at any time. It's not easy and it's not nice but I'm responsible for results and performances.
"If the crowd see performances like that, I'm going to get hammered and I accept that."