Derek McInnes thanked the City supporters for their positivity after his side extended their winless home run to nine games at Ashton Gate.
Visitors Derby County scored twice in three first half minutes and eased to a comfortable 2-0 victory to end a sequence of four straight defeats on the road.
Sam Baldock went close to halving the deficit before the break and Liam Fontaine was denied from point-blank range late on, but City never really threatened to mount a serious fightback.
Nevertheless, the Robins were still applauded off at full-time by sections of the home crowd – something the manager said his players should be “embarrassed” by.
"I thought the support was brilliant today. The fans applauded the players off the pitch and I thank them for their backing,” McInnes told Bristol City Player.
“The players should be embarrassed by that, because the fans deserve better.
"Once again the manner of the goals, leaving players unmarked inside the penalty area, is poor.
"And they came in the space of three minutes – we seem to be vulnerable when we concede once and that showed again.
"We lacked the ability to really punish Derby from the chances we created. If we got one, we had a chance, but Derby earned the right to defend their lead and they've run out deserved winners.
"We created good opportunities, but whether you take them or not can be the difference, which we’ve seen today.”
The Scot was left short of options after the interval having already made two of his three substitutions.
The first, a tactical switch, saw Greg Cunningham come on for his return from injury in place of Matthew Bates, before Ryan Taylor was replaced by Steven Davies at half-time.
McInnes added: "We needed more attacking play from our full-backs and that was the reason behind bringing on Greg for Matthew Bates.
"But then Ryan Taylor came off injured at the break and that made it tough for us, because there were times when they were defending deep and we needed to get the ball forward quickly and needed a target man to hit.”