Gabriel Agbonlahor got the only goal of the game in the first half to end a five-game winless run, with the returning Christian Benteke and Ron Vlaar playing an important role in the victory.
"I thought we played really well and it could have been more," Lambert told Sky Sports. "Even in the first half we had some really good chances. It could have been three or four.
"We've been without a couple of big players with Benteke and Vlaar coming back. Agbonlahor has been missing at times. Delph has been missing.
"We needed those big players back. When you lose Benteke and Vlaar, that's a big chunk of your side. It's been hard. After the criticism of late, that (win) was well justified.
"We have found it hard to cope with those injuries but when we've got everybody fit we're a really good side. I'm delighted as it's a hard place to come and they're fighting for their lives.
Vlaar had to be substituted in the latter stages of the game and Lambert is hoping the Villa captain will not be missing any further matches.
"He was feeling his calf," added Lambert. "He only trained for the first time the other day but, to be fair, he put himself forward. Hopefully, it's not too bad."
With the January transfer window now open, Lambert also admitted that he is looking to bolster his squad with some experienced players.
"If we can give them a helping hand in January with a bit of experience, we'll certainly try and do something," said the Scot.