Supporters from both teams stormed the pitch at the final whistle, which has led to a reported 17 arrests.
"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," a club statement read.
"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."
On the pitch, Jay Emmanuel-Thomas opened the scoring with a 30-yard thunderbolt.