Silva was at fault for the second of West Brom's three first-half goals at The Hawthorns, as the Blues had to fight back from an error-strewn opening 45 minutes to draw 3-3 thanks to Mason Mount, Callum Hudson-Odoi and Tammy Abraham.
It was the veteran defender's first action in the Premier League at the age of 36 and it was an unfortunate slip in an otherwise steady top-flight bow.
Chelsea boss Lampard said Silva is experienced enough to own up to his mistakes without the need for him to pile in too.
"Listen Thiago Silva is going to be fantastic for us, he's been incredible in his career," Lampard told a post-match news conference.
"I will not look at him, I can talk about the mistakes - they're clear and we have to be open and honest about that, but I'll not put any blame on him. We're a team that has to react around that and to be fair the team did in the second half.
"It's nothing on Thiago, I'm sure he'll stand up and say it was a mistake, other than that I thought he was faultless in the game.
"That's his first Premier League game done and in the bank, we'll get more from him as he gets fitter and the team gets fitter."
Chelsea's equaliser had a hint of fortune, with Kai Havertz potentially handballing in the area in the build-up.
West Brom boss Slaven Bilic, who also felt there a was a foul prior to Hudson-Odoi bringing it back to 3-2, had no doubts the gal should have been chalked off.
"The third goal is very difficult to accept," Bilic said. "For me that is so clear that I don't even want to talk about it, it is obvious.
"It's not maybe, it's not possibly handball, it is handball that's end of story, full stop. How someone can say that's not a handball is beyond me."