The Scot, who is poised to sign a new contract, has guided the Canaries to back-to-back promotions, the first club to do so since Manchester City in the 1999/2000 season.
Lambert told the club`s official website: "It's been an unbelievable season. To get an award like that after last year's is an incredible thing.
"Last year we had to find our feet and what has happened has been an absolutely incredible journey. Two years on the bounce we've done this, back-to-back promotions are very rarely done. The last one was 11 years ago which is incredible. It's just been a massive, massive season for us.
"I just think the team's going well and we're doing all right and the biggest thing was to get out of the league, which we achieved and it's an award that will be really, really nice. As I've said, though, you don't get that without the players and the staff I've got. It's an award for everybody these sorts of things - and what we've achieved and what the lads have achieved is just incredible."
Meanwhile, second year Academy scholar Matt Ball has signed a one-year professional contract with the club, the 18-year-old saying: "I'm very happy, obviously the club is moving forward and I want to be a part of that. I'm very honoured to be given the opportunity."