Only four minutes of stoppage time were signalled, but more than seven had been played when City won a free-kick on the edge of the visitors' box. The final whistle only went when Nicky Shorey's shot was blocked by the defensive wall.
Dunne said: "I'm frustrated because we aided the referee in adding on the time. I am not into time-wasting and we brought what happened at the end on ourselves.
"Generally, we should be very pleased with our performance. We were missing 10 players coming into the game and our youngsters did well.
"We knew Bristol City would have a lot of possession and we let them have it in certain areas of the pitch. On the counter attack we were very dangerous and I thought our back four were outstanding.
"City had a bit of momentum in the second half and we needed to see it out, but we paid for one momentary lapse in concentration."