Villa raced into a 2-0 lead thanks to goals from Andreas Weimann and Christian Benteke, but Daniel Sturridge reduced the arrears with a goal back for Liverpool right on the stroke of half-time.
Liverpool won a controversial penalty early in the second half when Luis Suarez went down in the box under a challenge from Brad Guzan, but Lambert felt his goalkeeper did not touch the Uruguayan in the incident.
"I think Guzan pulled his arms away, that could be a biased view, but I don't think it is," Lambert told Sky Sports.
"I think [referee] Jon [Moss] is in a good position to see it but if you look at Guzan he pulls his arms away, and I am sure everybody will have a different opinion but my own view was I think he pulled his arms away.
"Listen, you are up against the Kop End and it can be an intimidating place.
"Jon's got a hard job, he has got one decision to make, but I don't think it was [a penalty]."
Lambert was delighted with his side's display as they dominated for long periods of the game and felt they 'should have been out of sight' in the first half.
"I thought we were outstanding to be fair," added Lambert. "I thought first half we should have been out of sight.
"I thought maybe we should have been three [up] at least anyway, but the way we played the game was absolutely fantastic.
"Terrific performance, big, big performances and I am really happy with that."