Doncaster are investigating reports of "unruly behaviour" among some of their fans during Saturday's match at Hartlepool.
A statement on the club's official website confirmed that bans would be issued "wherever appropriate" once the investigation into "crowd disturbances" had been concluded.
The statement added: "Individuals, supposedly 'supporting' DRFC, engaged in aggressive behaviour at the ground which has severely damaged the reputation which true Rovers' fans have enjoyed over many years.
"In support of the Football League's campaign to eradicate abusive and aggressive behaviour within football grounds, DRFC condemns the actions of any individual(s) behaving in a manner likely to jeopardise the safety or enjoyment of others in attendance, and thus tarnishing the reputation of the club's travelling contingent of excellent supporters."
Earlier this month the club released a statement to condemn the actions of a fan who had vandalised a toilet block at Leyton Orient using human excrement.