There were 12 City and six Rovers fans arrested at the first meeting between the sides in almost seven years at Ashton Gate on Wednesday evening, while 16 people were injured including one police officer and a steward.
Up to 50 seats were torn out and both managers, City's Sean O'Driscoll and Rovers' John Ward, were quick to express their disgust at the scenes at the Johnstone's Paint Trophy match.
On Thursday the Robins released a statement promising stiff action against any proven offenders.
"Bristol City Football Club totally condemns the actions of spectators who invaded the pitch at the conclusion of last night's game with Bristol Rovers at Ashton Gate," the statement said.
"The joy of winning the first competitive Bristol derby in six-and-a-half years should have been remembered for all the right reasons. Instead, actions from the minority of the near 18,000 crowd has thrust the club into the national media's eye for the wrong reasons.
"This sort of behaviour is unacceptable and cannot be tolerated. We believe strongly Bristol City is a family friendly club, which is safe for supporters of all ages.
"We will be working closely with the police and authorities, including the use of CCTV and imagery, to help identify those involved.
"Bristol City Football Club will take the strongest possible action against anyone found guilty of violent conduct - for the club, our supporters and the city of Bristol."
City manager O'Driscoll said after the match: "The scenes at the end were disgraceful. It's taking the shine off a good victory for us. That's what people will be talking about - not the game.
"What's happened is what we didn't want to happen and the players are all disappointed as well. The game was played in a good spirit, competitive and not over-zealous, and we wanted the supporters to act in the same manner. Unfortunately they didn't."
O'Driscoll added: "The scenes at the end ... you'd think we'd got promoted to the Championship and not the second round of the Johnstone's Paint Trophy. That's the shame of the whole thing - it's ridiculous."
Rovers boss Ward said his team were unfortunate not to have taken the tie to a penalty shoot-out.
"However, given the pitch invasion at the end of the match it was probably good that the game didn't get that far," Ward said.
"You don't want people on the pitch, it's all about the players. It's ridiculous that they come on the pitch and goad opposition fans, and why people can't behave themselves at a football match is beyond me.
"I think the players on both sides were terrific, but I feel the supporters were disappointing."
Police said the build-up to the game was peaceful with both sets of fans well-behaved and in good humour, but as fans began to enter the stadium isolated pockets of anti-social behaviour broke out in and around the ground.
Chief Superintendent Caroline Peters, match commander, said mounted police assisted stewards in clearing the pitch of supporters, which took a matter of minutes.
"The majority of fans were well behaved and enjoyed the match," she said. "However, there was a small minority who came with the sole intention of trying to spoil the enjoyment for the majority.
"We warned before the match that we would not tolerate any form of anti-social behaviour or violence.
"We will now aim to bring the offenders to justice using CCTV coverage and other intelligence and information gathered tonight to bring the offenders to justice."