However, Lambert believes that his side have been playing better than their results suggest, and that they can be proud of their performance against City.
"I cannot fault the lads. We have been playing very well without getting the rewards we deserve," said Lambert.
"We were in the game for long periods and everyone is disappointed to lose. We had one or two little half chances, but we were against a good side. We came away with our heads held high.
"The players know they are playing well. It is different if you have been done heavily. We will keep playing and hopefully the rewards will come."
Villa defender Ciaran Clark claimed that he had been fouled in the build-up to City's goal, but Lambert admitted it was a fair tackle.
"I did not think it was a foul. When you are a defender and you are near enough last man, you do not take any chances," he added.
The defeat means that Villa have won just one of their last 11 league games.