Alan Lee and Danny Ward scored late goals to cancel out Scott McDonald's opener and secure the win at the John Smith's Stadium, and the Boro boss was evidently frustrated with the scoreline.
"This last six weeks has cost us and we keep conceding goals that we shouldn't concede," Mowbray said.
"We have to improve drastically. The players need to do their jobs. We are being naive and it's happening too often.
"Whatever league you play in - whether it's the Conference or the Champions League - if you can't defend set-pieces you are not going to win matches.
"I wouldn't have been happy with a point but to lose the game is unbelievable. There was not a lot of quality but we came in with a clean sheet at half-time," he said.
"Then we got the goal and had a few half chances and looked reasonably comfortable. Then with a corner kick and a header and they are back in it.
"We have to analyse it and work out how we put it right."