After wins against QPR and Newcastle, Saints came into the game with heightened expectation and new-found momentum.
Nigel Adkins' side were on course for another three points when Lambert prodded home his sixth of the season, but Robert Snodgrass' leveller earned the Canaries a 1-1 draw and a point.
"I am definitely frustrated not to get the three points," Lambert said.
"I thought we played really well in the first half and I thought we were definitely going to win it.
"We've come in disappointed at half-time and felt we could have pushed on in the second half.
"We haven't managed to do that so, yeah, I am disappointed."
Much of the talk before the match surrounded Mark Clattenburg, who returned to frontline refereeing for the first time since Chelsea alleged he racially abused John Obi Mikel against Manchester United.
Norwich manager Chris Hughton and several players were frustrated he missed Lambert's handball in the build-up to the opener, although the striker laughed off his role.
"I am not sure exactly where it hit me but obviously I just carried on and put it in the back of the net," he said.
"Obviously I am just looking at the ball, it's hit me and it has landed there. You've just got to play to the whistle."
As well defending himself, Lambert stood up for Saints goalkeeper Paulo Gazzaniga.
The 20-year-old Argentinian has been found wanting on several occasions this season and was at fault for Snodgrass' leveller, with the midfielder's free-kick somehow beating him at the near post.
"He didn't have to apologise to us," Lambert said. "You could see he was disappointed.
"He has done really well the last few weeks and it was a just little lapse in concentration.
"He is more disappointed than us and these things happen. It is how you respond to it."
The draw extends Southampton's unbeaten run to four matches and Norwich's to eight in all competitions, much to manager Chris Hughton's delight.
"I think it was a fair result," the Canaries boss said. "I thought Southampton were better in that first period and we took a little bit of time to get going.
"We were stung a little bit by the goal, but I thought we were very good in that second half.
"As the game opened up, I thought we defended very well and if anybody was going to score on the break I thought it was going to be us.
"I think it was nothing less than we deserved, to get back into the game."