The Reds fought back to win the FA Cup tie at Shrewsbury, despite the shock of Daniel Udoh's goal.
A small minority of fans were condemned by the club for their vile chants.
A group of Shrews fans were filmed on social media singing songs about the disaster in which 97 fans died.
"These people do not represent our club in any way, shape or form," the statement said.
The third-round tie was tied at one point.
"Shrewsbury Town Football Club is disgusted and appalled to see and hear the reports on social media about the vile and offensive chanting and behaviour of a very small minority of our'supporters' yesterday," the statement said.
We are working with West Mercia Police to try and identify those responsible.
If any supporters have any information that could help us identify those responsible, they can contact the club and we will use the information as part of our investigations with the police authorities."
Burgoyne said that any supporters involved should be ashamed and banned from the club for life.