Goals from Youssouf Mulumbu, James Morrison and Paul Scharner overshadowed Jean Beausejour's effort and sealed victory for the Baggies, who have moved above Blues in the battle for Barclays Premier League survival.
The Blues boss said after the game: "Wembley was a factor in our performance.
"To make the enforced changes we had to do made it very difficult for us. You are looking for the guys who come in to provide fresh inspiration, but it did not materialise, and the goals we lost were schoolboy errors.
"It is a kick in the teeth, and we know the battle we face, and we will see where we are in May."
"The boys were aware already that they are in a relegation battle. It is not a case of it just creeping up on them. This is not a wake-up call.
"We had to make all those changes, and there will still be major doubts for the game at Everton in midweek.
"But, I still back this team to come back from this."
Source: PA