Scott Hogan was the match winner as his hat-trick secured Birmingham's first victory at the Hawthorns in over 17 years.
West Brom players were booed off the pitch, with the defeat keeping the Baggies down in 20th spot.
After the match, Bruce slammed his players for their display, saying: "We didn't take part in the game until the last 20 minutes.
"In a big derby we were found short. We didn't win a challenge and we didn't deal with Troy Deeney and the physicality of Birmingham. We were nowhere near where we should be.
"Individual errors are something you can't fix. The concentration of the defenders was awful and the goals were something you'd see on the schoolboy pitch with 11-year-olds.
"When you defend as hideously as that, you're in for a poor evening. It was awful. What we witnessed in the first hour was scandalous."
The Baggies have won just one of their nine games this season and face a big test against second-placed Norwich City on Saturday.
Birmingham, on the other hand, are up to 14th in the standings after picking up their second successive win.
Manager John Eustace praised his hat-trick hero, saying: "Scott Hogan is a top, top striker. The one thing I was excited about coming here was that I've worked with Scott at international level and I know what he can bring to the Championship.
"You don't have moves like he's had if you're not a top striker. The lad just needs confidence but you can see he's a top, all-round player.
"The way he took his hat-trick was three different finishes and it was brilliant."