The 3-2 loss leaves Villa languishing just above the relegation zone but Lambert was delighted with the courage shown by his team against the league leaders.
"I am gutted to lose but I am absolutely proud of them," said Lambert. "To play against the calibre of the opposition we are up against and perform as we did was fantastic.
"Even when they got back into it the game we still had chances to win it. It was great courage to come back, we played some incredible football, I thought we were excellent.
"We gave it absolutely everything, we were brilliant. I can't fault the team. We've got lots of young lads in the team and they were great. I can't ask for any more from them.
Villa have only recorded two victories in 11 games this season.