The Hawthorns was silenced by a ruthless first half from Lambert's visiting Villans, who went in at half-time two goals to the good courtesy of Christian Benteke and Gabriel Agbonlahor strikes.
But the Baggies surged back in the second period with Chris Brunt halving the deficit four minutes after the break and, just when it seemed likely Villa would ease their relegation troubles with an away victory, Peter Odemwingie ensured a draw.
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."
On the eye-catching performance of Charles N'Zogbia, the Scot added: "Charles is a real talent, a real, real talent. He goes past people as if they're not there at times. When I took him off, he wasn't injured. He's back from a long lay-off so you have to watch him.
"We have games coming up. We have to protect him."