Chelsea fell 3-0 down before half-time after a disastrous first half, where Callum Robinson and Kyle Bartley both profited from defensive errors from Lampard’s side.
Mason Mount, Callum Hudson-Odoi and Tammy Abraham dragged Chelsea back into the contest in the second half, with Abraham equalising deep into stoppage time to rescue a point for the Blues.
Lampard felt as if it was two points lost for his side, however, and was hugely frustrated by the catalogue of errors made by his troops.
Silva was at fault for Robinson’s second.
The Brazilian centre-half, 36, sloppily let the ball roll under his foot and Robinson charged through to fire past Willy Caballero to double West Brom’s lead.
Silva was then hauled off midway through the second half as Olivier Giroud was thrown on as Chelsea chased the game, but Lampard knows that he won’t need to give the defender a dressing down for his mistake.
‘Thiago one is a mistake,’ Lampard told Sky Sports after the match.
‘He’s been there long enough to know one, we’ll certainly give him that one in his first game.
‘And then Marcos loses his man from the third goal from the corner. It was mistakes, clear mistakes [that cost us].
‘It is two points lost at the end of the day – and that’s no disrespect to West Brom. You come here and you know the transition and any mistakes would be something they would jump on – that and set pieces. You can’t legislate for the mistakes that there were today.
‘We created two or three great chances in the first half. I felt we would create more, the only other problem at 3-0 was West Brom were going to protect their lead more. It is a big lesson for us.
‘We will get a lot better, we’re still finding our way with new players and a lack of pre-season. Today is part of the process of getting better.
‘There is a lot we can keep getting better at. I’m not going to criticise every part of our game, I think they had three shots on target and got three goals.
‘There were genuine mistakes. There was nothing tactically you can analyse again and again – there were just pure mistakes.’