The London outfit went down 2-1, with Marlon Pack and Jamie Paterson scoring in the first half before a stoppage-time consolation goal from Idrissa Sylla.
Former Bristol Rovers player and manager Holloway was mercilessly baited by home fans throughout and made no attempt to disguise his feelings after the game.
"How do you defend the indefensible," he said. "I like my teams to represent my character and I have never gone down with a whimper in my life.
"Some of the things I saw in the second half were incredible. When you are 2-0 down and you get a free-kick surely you run to the ball and take it as quickly as possible.
"Twice we allowed City players to pick the ball up and walk backwards with it. One got booked for time-wasting and the other didn't, but where was the fight from my players?
"People inside this ground know that when I wore the blue and white quarters (Bristol Rovers colours) I would never have allowed that sort of thing to happen.
"City didn't even have to work for their goals. We need another win to be safe and we have been trying to get it for four games now."
City took a 14th-minute lead when Pack lashed in a right-footed volley from 15 yards and doubled their advantage five minutes before the interval, Paterson racing onto a Matt Taylor pass to beat the advancing Alex Smithies.
Although Rangers improved after the break, they rarely looked like scoring until the final minute of injury time when substitute Sylla shot home from a Conor Washington cross.
Home boss Lee Johnson was delighted with his team, who climbed to 18th place, but remain only four points clear of the drop zone.
He said: "I thought the attitude of all my players was first class. We won the battles and deservedly took the points.
"Nothing is decided yet, but I know my team and I have a good feeling about where they are at the moment.
"Nothing is settled yet and we have a hugely important match at Blackburn on Monday. We will go there to win the game, even though a point would not be a bad outcome.
"Frank Fielding has made one really important save for us today, but I thought the back four in front of him were outstanding.
"Now we have to take our home form into an away fixture. If we can do that we are capable of winning at Blackburn."