Rangers chief executive Martin Bain and Celtic counterpart Peter Lawwell say much of the debate after last week's Old Firm game was "ill-informed".
And both insist that problems associated with the Old Firm fixtures are societal issues.
However, Bain and Lawwell gave a commitment on behalf of their clubs to do their part to tackle the problems.
The pair were speaking after a summit to discuss Old Firm-related disorder with police and the First Minister.
Scotland's football authorities were also in attendance at the summit in Edinburgh.
"There has been an extraordinary amount of debate since last Wednesday's match, much of it ill-informed," said Bain.
"There are undoubtedly major issues for society in Scotland and with the best will in the world they cannot be blamed on a football club or cured by a football club. We will do everything we can to help.
"As a club we strive to set the best standards possible and will continue to do so. We have a responsibility.
"At today's summit we stressed the considerable efforts our clubs make, individually and collectively, on a daily basis to deliver real benefit to people and communities in the west of Scotland and beyond.
"It is our intention to continue and build on that work.
"As leading clubs we are acutely aware of our responsibilities on and off the pitch."
Lawwell added: "It is very important that events of last week are given perspective and are put into context.
"While the club recognises all that happened last week, much of what has been said has been disproportionate and ill-informed.
"Celtic Football Club is recognised throughout the world as having the highest standards and we aim at all times to live up to these standards.
"While many of the issues surrounding the Celtic v Rangers fixture have been blamed on the clubs, clearly there are a number of societal issues which need to be addressed.
"Celtic has and will continue to address these.
"How much more can the clubs do? We need help. The stigma always attaches itself to Celtic and Rangers.
"How much more can we physically do?"
The Old Firm have jointly issued a six-point plan aimed at addressing problems arising from the derby, including measures to tackle sectarianism, drink-related offences and domestic violence.