Real Madrid asked the organizers of the Champions League final for answers about the measures taken to protect the jahour in the match in Paris, which saw riots.
The kick-off, which ended with Real Madrid's 1-0 win over Liverpool, was delayed for more than half an hour, after French police confronted fans who wanted to force their way into the stadium without tickets.
Riot police fired tear gas at fans, including women and children.
French Interior Minister Gerald Darmanan said Liverpool fans were responsible for most of what happened, saying that 30,000 or 40,000 of them did not have valid tickets to the match, causing chaos.
The Liverpool crowd responded by saying that most of the English fans had acted responsibly, but were treated harshly by the French riot police.
"We want to know why the stadium was chosen to host the final and the criteria for the selection in light of what happened on this day," the Royal Club said in a statement.
The European champion added: "We are also asking for answers and clarifications about those responsible for leaving the public unprotected or guarded, although the public's overall behaviour has sometimes been exemplary."
"Based on the images provided by the media, it is clear that many fans have been beaten, prosecuted and abused."
On Thursday, Liverpool CHIEF EXECUTIVE Billy Hogan repeated the call for an investigation into the events, saying the abuse had affected fans of both teams.
Uefa has launched an independent investigation into the incident, while French Sports Minister Emily O'Dea Castera said Monday that her country would issue a report on the events of the match within 10 days.