Southampton were cruising at 3-0 on the south coast before two late defensive lapses allowed the Canaries to score twice in a minute and give the visitors hope of snatching an unlikely point.
But Steven Davis' swift counter-attack allowed Sam Gallagher to score from close range and lift Southampton into eighth place in the Premier League.
"Within a minute we'd gone from dominating the game completely to them trying to equalise, that's what happens in football." said Lambert, who scored within 65 seconds of replacing Adam Lallana to put the hosts 2-0 ahead.
"It was a strange game. It would have been very interesting in the dressing room if we'd managed to lose a three-goal lead, but we won, that's all that matters.
"It was a good display apart from the last five or ten minutes."
Southampton visit Tottenham next week with an outside chance of qualifying for the Europa League next season.
"We're not giving up on anything," added Lambert. "I'd be lying if I said we were aiming to catch Tottenham in fifth place, but we do play them next week and we will be trying to win the game and to finish as high up as possible."
Roy Hodgson was present to see Lambert score and the striker still has hope of making England's World Cup squad, adding: "It's my dream and everyone's dream. I am always pleased to score in front of anyone."