The 2-0 defeat at the Hawthorns was Bruce's first managerial defeat in a local derby since he guided Blues to promotion to the Premiership almost three years ago.
"We were second best in every department from the first whistle to the last," the Blues boss told Sky Sports News after the game.
"Two or three weeks ago we looked a very good team against Liverpool and now in two away games against Crystal palace and West Brom we simply weren't good enough.
"I've asked a few questions in the dressing room and its not often, or ever, that I have to publicly criticize people but I simply won't put up with performances like that, thats for sure!
"We were thoroughly beaten by the better team on the day, who had more about them, in every department.
"We were a sorry second best and I can only apologise to the fans that came to support us.
"It's not often in the last three-and-a-half years that I have had to come and apologise for a team of mine that have just rolled over like they did."