Charlie Mulgrew said that the players take responsibility for the second half of the collapse, so they were defeated for the first time this season.
Mulgrew scored directly from a corner and gave Rovers the lead in a first half in which they had excellent chances.
However, they would be the same after Josh Brownhill made a free kick before the Robins scored three runs after the break and lost 4-1 winners.
And Mulgrew admits that the second half was undersized by Rovers who were well defeated at Ashton Gate.
"We never had the chances we had in the first half," said the skipper after only a second loss since February.
"They have the blocks and saved and we do not.
"We all take responsibility and look forward to continuing as soon as possible.
"We started reasonably well but did not finish it well.
"That shows what the championship can do."
Kasey Palmer hit the post with a score of 1-0, while Adam Armstrong also had an excellent opportunity after Brownhill was leveled.
But Mulgrew felt that the City equalizer was a runaway battle for Rovers, with boss Tony Mowbray feeling that they had at least two goals for the good in the rest instead of the level.
Mulgrew added, "I think we had two or three good chances and that they got the blocks and saved them.
"It took the stuffing out of us when they scored that free kick.
"There is no excuse for us to give away the goals we have and we still thought we could have done better.
"There we will take the bones, pick ourselves up and go again after the break."
"We now have a break, we probably prefer to go again, but have to pick ourselves up when we come back.
"We have to pick ourselves up and look forward to going again."
Mulgrew scored straight from the corner in the 13th minute to put Rovers ahead.
His inswinger defeated the defender on the first post and caught goalkeeper Niki Meanpaa to nestle in the far corner.
When asked if he had ever done it before, Mulgrew admitted that he had done so, referring to a goal for Celtic in 2013 against Ross County.
"The first time we had not worked on it, while we were crazy enough this time", said Mulgrew, who is now going to work with the national team Scotland for their upcoming matches with Belgium and Albania.
"It is something that we had done on the training field and thought that there was a chance.
"Fortunately, it went well."
Boss Mowbray transferred the changes in the second half and sent three attacking players to the new signing of Ben Brereton, striker Joe Nuttall and Joe Rothwell.
"The first 60 or 70 minutes I thought we were good and deserved more than we have, but you have to accept that football can be cruel and that's it," the boss added.
"I think that until their second goal I thought we were okay and could win the game.
"Yet this team has not often been on the losing side.
"The last twenty minutes we had to be better in my head, but we had a lot of strikers on the field and the frustration, the last 20 minutes."