Christian Benteke put Villa on course to move out of the bottom three, but second-half goals from Darius Henderson and Steven Gerrard won it for the Reds.
Lambert has seen his side climb out of the relegation zone on four occasions this season and continues to take heart from their performances.
He said: "For 45 minutes we were excellent, we competed brilliantly, we looked a threat every time we went forward against a really good side.
"The goal two minutes after the restart was disappointing to lose. But we are playing well enough to win games.
"We are four points from 11th place. There's going to be some twists and turns.
"The thing for myself is that in spells we are playing really well and confidence is a big part of the game of football.
"If you keep that, then that will certainly help you."
Villa have gone 20 games without a clean sheet since the goalless draw with Stoke on December 8.
Lambert said: "If you can get a clean sheet and win 1-0 you would take it. To do that, it will be great."