Saturday's game at Turf Moor was called off on 'police advice' after fans of the German side started throwing seats at Clarets fans after Sean Dyche's side took the lead.
During a discussion in Dusseldorf on Monday, Cologne sports director Jorg Schmadtke called on the DFB (German FA) to do more.
'Ultra groups are being formed across the country and we will need to find answers,' he explained.
'The clubs can only deal with the groups around them and try to influence them. But stiff fines from the DFB were not necessarily the solution.
'The way the DFB is doing things at the moment, with these various sanctions, we will not stop the cycle. It is not improving the atmosphere.
'But we, the clubs, won't be able to do so, on our own. The DFB (the German Football Association) as the umbrella organisation and the DFL (the German Football League) need to get on board.'