Match Commander, Chief Superintendent Shaun Morley, also thanked the vast majority of fans for their cooperation during the police operation.
He said: “Overall, the behaviour of the fans from both teams attending Bramall Lane last night was incredibly positive and there was real excitement surrounding this fixture.
“As both sets of fans were heading to the stadium, there was some disappointing behaviour by a minority of fans that involved a flare or firework being thrown, as well as some plastic cups/bottles.
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“The use of pyrotechnics is incredibly dangerous and someone could have been seriously injured. In response to this growing risk to the safety of all fans, additional officers were sent to the stadium to help make sure all fans got into the ground without further issue.
“After the match, there were a couple of minor incidents of conflict between both sets of fans on Bramall Lane, which saw some antisocial behaviour and poor behaviour – again from the minority.
“We received one report of assault that we believe may have been connected to the derby, but an investigation is ongoing into the circumstances surrounding this incident.
“We also had one officer suffer minor injuries during the initial disturbance pre-match.
“Overall, the fans that attended the match this evening did so in high spirits and I thank you all for your patience while we managed the dispersal of over 30,000 people out of Bramall Lane into the city centre and beyond.”
Six arrests were made over the course of the operation for a range of offences, including being drunk and disorderly, public order and assault.
In addition, a number of Section 35 notices were issued.
Chief Supt Morley added: “Further enquiries will continue into those incidents where individuals were arrested and if anyone has any concerns or wishes to report any instances of criminality from this evening’s event, please call 101 or Crimestoppers anonymously on 0800 555 111.
“However, the fact that so few people were arrested out of a crowd of over 30,000 is testament to the positive attitude of Sheffield football fans and your support of the policing operation.
“There continued to be a police presence in the city centre to ensure the safety of everyone who is enjoying the city’s nightlife, which also passed without major incident.
“I’d also like to take this opportunity to thank all the officers and staff that worked on this operation and played their part to keep people safe, with special mention to those officers who joined us on mutual aid from forces across the country.”