Gabby Agbonlahor proved to be the matchwinner after bagging his first Premier League goal since last November to ruin former manager Martin O'Neill's day.
The striker fired home from close range just before the hour mark to claim just a second league victory of the season for the dynamic midlanders.
And Lambert told Sky Sports: "I thought we deserved to win the game. We were up against a really good side and it really is a hard place to come, but we just edged it and I thought there were some massive performances."
Asked if that was the best he has seen of his team, Lambert said: "I think as a whole, although we played well against Swansea and West Brom for certain parts, on the day I thought we were outstanding."
And on the performance of midfielder Ashley Westwood, who the club signed in the summer from Crewe, he added: "You'd think he's played at this level for five years and hopefully the way he's performed today and the way he slotted in, I thought he was excellent.
"It's unfair for me to single out any individual. I think as a team, and the spirit they showed, they were outstanding. It was a tough game, but it was also a massive win for us."