City's equaliser came when referee James Linington pointed to the spot after Cedric Kipre's clumsy lunge on the falling Koji Miyoshi and Juninho Bacuna scored from 12 yards.
From that moment, John Eustace's hosts did not look back and Dion Sanderson headed the Blues in front in the 38th minute before substitute Gary Gardner sealed victory with an 87th-minute freekick.
Birmingham went fifth in the standings with the win, nine points behind leaders Leicester City, while West Brom dropped to seventh.
"Today we competed against more than just 11 players," an angry Corberan said.
"It's difficult to analyse the game without talking about the penalty because it changed the game.
"When you're a coach and you put your life into this work - and I put my life into this work - how do you feel?
"It was one action where the player (Miyoshi) slipped in front of Kipre, you have to consider if it was a penalty.
"In a month's time, no one will remember this, but I will never forget this. This action has had a massive impact.
"I feel emotionally it affected the concentration of our players because in football and in life when something is unfair, it's difficult to accept."
John Swift put WBA ahead in the fifth minute with his sixth goal of the season.
Then came the hotly-disputed equaliser in the 23rd minute, with Bacuna sending Alex Palmer the wrong way for his first Championship goal of the season.
Birmingham went ahead when Dion Sanderson guided a header high into the net from Cody Drameh's deep cross before Gardner curled home a delightful free kick from the edge of the area.
"I think it was a true Birmingham City performance - we played some exciting football at times but we had to dig in and fight at times and that togetherness is what this football club is all about," Blues manager Eustace said.
"We had to do that at times and I couldn't be any prouder of the players and the fans.
"Tonight was a special night - we were playing West Bromwich Albion at home in front of a full house, live on the telly and it was a big game."
