The result has temporarily moved Norwich up to third place in the Championship table, with Adams's side trailing leaders Derby County on goal difference.
"I thought we looked sharp and lively and could have had more. Bolton scored a late goal to give us butterflies, but I think we were value for money," he told Sky Sports News. "A win is a win and I think we deserved it.
"They had a lot of the ball and we had to defend. I thought we were excellent and yes, we want to attack and score, but sometimes you have to win when teams come at you."
Norwich continue their Championship campaign on Tuesday when they travel to promotion rivals Middlesbrough.