Friday night’s match at Easter Road saw Rangers captain James Tavernier confronted by a Hibs fan who invaded the park.
This is the latest in a long line of incidents involving misbehaviour from supporters throughout the Scottish football season.
The issue in the sport was highlighted further when Aston Villa’s Jack Grealish was punched by a Birmingham supporter during Sunday’s derby clash in the English Championship.
Blackford, who is the All Party Parliamentary Group for Football Supporters vice-chairman and a Hibs fan, said: “We have to accept that we have a real problem in football at the moment and we have to deal with it. There has been a decline in standards that I’m afraid to say can be seen in society in general.
“I was very pleased to hear Hibs chief executive Leeann Dempster speak out against what happened at Easter Road on Friday but if football cannot deal with these issues - and we have witnessed an increase in the number of sectarian incidents, too - then we might have to consider fresh legislation.
“We cannot just stand by and not take this seriously. We are talking about player safety here.
“I am old enough to remember non-segregated crowds in Scotland. I remember going to Edinburgh derbies in the 60s with my uncles who supported Hearts. I know why that had to change but there is something very wrong if going to watch football cannot be a safe and joyful occasion for everyone.
“The clubs have to accept responsibility for how fans behave at their games. I know why clubs and the football authorities don’t want to do that but it is time to talk about strict liability for clubs. That is how behaviour will improve.”