McLeish admitted his side paid for some sloppy mistakes as Albion recovered from a 1-0 half-time deficit.
He said: "I am stunned by the mistakes we made, human errors.
"I've been telling you every week about the character in this team. Today that wasn't evident in the second half, unlike us.
"West Brom changed their shape which I thought they might do but it was very unlike us to capitulate.
"The mistakes gave them a way back into it, nothing to do with systems, and after that we were never really at the races.
"It was very untypical of this team. We said that in the dressing room and some of the players admitted that as well."