The National Professional Football League (LFP) attempted to postpone Deportivo's fixture with Atletico Madrid on Sunday, following violent clashes between the two sets of fans in the Spanish capital.
The result of the violence was one fatality and reports of 11 more people injured.
Real Madrid boss Ancelotti - who has coached in Serie A, the Premier League and Ligue 1 - said the LFP needed to emulate strategies in place elsewhere in Europe, notably England, to cease fans from fighting prior to fixtures.
"I had already experienced this in the past, in Italy," Ancelotti said.
"Today is a very sad day as this is something everybody hopes will never happen. It is key that we all censor violence in sport, violence in football and violence in general.
"We all need to work together to try to prevent this happening again in the future.
"I have experienced managing in England and I think they have done a lot there to eliminate this shame from their football. They have done a very good job.
"They had terrible experiences with hooligans and by working together and implementing strict rules they solved this problem.
"I think both Spanish football and football in general should follow their lead and do the same so we can get rid of this shame."
Ancelotti claimed powerhouse clubs Barcelona and Real had taken measures to restrict certain people from entering their stadium, and also hailed the French league's stance.
"I haven't been here for a long time but I think Real Madrid have worked very hard," Ancelotti said.
"I think this club is a good example to follow, as well as Barcelona, since they did the same thing last year ['radicals' aren't allowed in the stadium].
"I think clubs can do a lot to prevent this from happening, they are doing a great job in France for example.
"Radical groups should be banned. A fan doesn't need a group to be a fan."
