Dean Whitehead scored the winner for Stoke with five minutes remaining of the game.
The Stoke boss told Sky Sports News: “We were desperately disappointed to come in at half-time just 1-0 up.
“When you’re on top of a game – and we were on top for a long time today – you’ve got to put chances away.
“And even in the second half we started really bright, had a couple of really, really good chances, then Ric scores a fantastic goal to make it 2-0 and you think ‘well, it’s over and done with.’
“But fair play to Birmingham, they did it Saturday (against West Ham) and they’ve not stopped again tonight.
“Its just lovely to see Deano score the winner.”