Two men, aged 31 and 47, were arrested in Birmingham city centre on suspicion of causing violent disorder following the match.
A 16-year-old boy was also arrested in connection with a public order offence.
Two people were taken to hospital with head injuries following the match.
West Midlands Police said that while in custody, the 47-year-old man had admitted possessing cocaine and received a police caution for that offence.
A fourth man, aged 19, who was arrested by officers patrolling the city in connection with an indecent assault in April 2014, was also released on bail.
The force said it was investigating allegations and video footage on social media suggesting some officers may have acted improperly in trying to contain the disorder.
"Officers are empowered to use force where absolutely necessary and it was a very tense event," said Ch Supt James Andrenov.
"But we expect really high levels of professionalism from all of our officers.
"They know they are accountable for their actions and we will investigate any allegations where inappropriate behaviour might have been exhibited by officers."
Three men arrested  in connection with disorder following Saturday's derby match between Birmingham City and Wolverhampton Wanderers have been released on bail.