The Barclays Premier League contest started disastrously for the visitors, with Albion frontman Shane Long netting in the third and 11th minutes, his second strike coming after he had collected the ball from a misplaced pass by Villa midfielder Leandro Bacuna.
But Lambert's men - given fresh impetus by the treble substitution he made in the 57th minute that introduced fit-again trio Andreas Weimann, Gabriel Agbonlahor and Fabian Delph to the action - recovered impressively after the break.
Karim El Ahmadi volleyed in from a Weimann header in the 67th minute and Baggies defender Goran Popov then inadvertently nodded Agbonlahor's 76th-minute cross to Ashley Westwood, who lashed a fine, swerving strike into the net from distance to level the match.
Reflecting on the encounter, Lambert said: "When you look at the start we had, it was really poor from our point of view.
"After around 10 minutes at 2-0 down, and particularly in a derby, you are up against it.
"But to be fair, I still thought we were seeing a bit of the ball, and at time you are thinking, 'Get them in at half-time, have a little chat with them'.
"They came out in the second half and I felt they were excellent.
"I thought they were well worthy of getting it back, and might have gone on to win it. The impetus was certainly with us.
"The first half wasn't good enough, but the second half was excellent."
Regarding the substitutes, Lambert added: "The three lads that came on had only started to train again on Friday and it was a big ask to put them in.
"I trusted the team I picked at the beginning to go and perform, and I always will do that and never have any regrets about any decision.
"But we needed a goal at a certain time of the game. I was actually going to put them on a bit later, but then we had a chat at half-time and decided to make the changes pretty quick. We threw them on and thankfully it worked."
Lambert singled out Westwood for particular praise, and not just relating to his goal.
"I thought Westwood was excellent the whole night," Lambert said.
"His passing was excellent and his goal was a fantastic strike - he has got terrific technique, and he is a terrific footballer, a really clever footballer. I thought he was outstanding."