A home date with the Reds was Villa's third in the space of eight days, and their third against a side expected to be pushing for a top-four finish this season.
Lambert's side have now suffered back-to-back defeats at the hands of Chelsea and Liverpool, but stunned Arsenal at Emirates Stadium on the opening day and are confident they can steer clear of the relegation troubles which haunted them in 2012/13.
On the performance of his side against Liverpool, Lambert told Sky Sports: "I thought in the second half we were excellent.
"We knew it was going to be a big ask. The three games we've had in a week's time have been huge. Nobody would have thought that we would have got any points, never mind anything else. We have always been in the games, which is fantastic for us, and have won one.
"It was a big ask, but I thought we were brilliant in the second half. Their goalkeeper has pulled off some brilliant saves from Chris (Benteke), one in the first half and one in the second half. Second half we were very good."
Asked if a third outing in such a short space of time had taken its toll on Villa, as they were sluggish out of the blocks, Lambert added: "I knew it would and the important thing was to get them in at half-time not conceding another one. But second half I thought we were excellent, we gave it a right good go.
"We are a young side, but I think the improvement is there for everybody to see.
"I can't be too critical of the lads because they have given me everything in the three games. They have got nothing to be ashamed of with the way they have performed in the three games. If we keep doing what we're doing, we'll have a good season."