The Midlands side entered the contest as the lowest scorers in the EFL this season, with just 16 goals to their credit, but were three to the good with less than an hour played in the six-pointer at St Andrew's.
"I'm gutted. You know you will lose games occasionally but it was the manner which was surprising, given where we are and who were playing against," Coleman told the Sunderland Echo afterwards.
"The lack of intent in our play all over the pitch was a huge disappointment and very worrying. You need a bit more courage, winning those tackles, that is one side of it. The other side is the courage to take responsibility, have that bit about yourself.
"I can only say it is unacceptable. We can't even begin to accept those defensive errors. If we'd come away losing, having had a go, that's one thing, but we didn't. It is hard to understand, we're in the bottom three, against a team down there, and we go missing for an hour. I can't accept that."
Next up for Coleman's side is a home encounter with mid-table Ipswich Town on Saturday.