Goals from Christian Benteke - his 10th of the season - and Gabriel Agbonlahor gave Villa a clear advantage at the interval.
But they were left to regret spurning other chances as Albion hit back to rescue a 2-2 draw through goals from Chris Brunt and Peter Odemwingie.
Lambert said: "I have a few things going through my head. I thought we were excellent in the first-half. We should have been out of sight, it should have been finished.
"We should have been four up. That would have killed the game. The way we played in the first-half was excellent.
"In the second half West Brom came out strongly but you expect that. They are the home side.
"It was disappointing not to win the game because it should have been finished in the first half."
A point was sufficient to move Villa out of the bottom three and Lambert insists they can survive.
He said: "I have always thought we would do it. I have always thought that.
"If you look at the league in mid-table, it's really, really tight."