The Blues suffered their 4th straight loss after a 42nd-minute goal by Lee Cattermole, who was left unmarked to head past David James from just inside the box.
Boro would have made the win more emphatic had it not been for a number of good saves from James.
"We showed no moral courage whatsoever," said Pearce. "If I was a supporter I would be disgusted. We were so spineless it was frightening."
Joey Barton was ruled out through injury while Sylvain Distin was suspended but otherwise only Andy Cole, out for the season, was missing.
And Pearce has told the City players to up their game or face being let go in the summer.
"If we get that kind of performance again there will be people leaving this club - make no mistake about that," he added.
"The buck stops with me. I'm the first one who takes the flak for it and I'm happy to do so, but behind me there are 10 players - I'll excuse the goalkeeper (David James) because there wasn't much more he could.
"None of the others stepped upto the plate, none showed any leadership or earned their wages."