The match, which Real Madrid won 1-0, was delayed by more than 35 minutes after Liverpool fans struggled to enter the stadium despite arriving many hours before the match.
Tear gas was used by French police, as supporters were detained in very compact areas around the Stade de France, prompting security fears to spread among those present.
“We are very disappointed with the problems entering the stadium and the breakdown of the safety perimeter that Liverpool fans have faced tonight at the Stade de France,” Liverpool said in a statement.
“This is the best match in European football and fans should not experience the scenes we witnessed tonight.
“We have officially requested a formal investigation into the causes of these unacceptable problems.”
The governing body of European football, UEFA, said the problem was caused by people without valid tickets trying to enter the stadium and using tear gas to maintain control.
“In the pre-match period, the turnstiles at the end of Liverpool were blocked by thousands of fans who had bought fake tickets that did not work on the turnstiles,” UEFA said in a statement.
“This created an accumulation of fans trying to enter. As a result, the start was delayed by 35 minutes to allow as many fans with genuine tickets as possible to access it.
“As the number outside the stadium continued to increase after the start of the match, the police dispersed them with tear gas and forced them to leave the stadium.
“UEFA is sympathetic to those affected by these events and will urgently review these matters together with the French police and authorities, and with the French Football Federation.”
The photos showed fans crammed into enclosed areas after a bottleneck formed around a specially tight entry point at the end of Liverpool.
Many fans with tickets say that they were prevented from entering the stadium in dangerous areas of people and that communication from security was poor.
“People without tickets forced the barriers and tried to enter the stadium to watch the match,” a spokesman for the Paris police headquarters told CNN. “These attempts created crowd movements.”
As the confusion spread before the start, videos surfaced on people’s social media, with no clear affiliation with a team, climbing fences around the stadium and running to the ground.
The match finally started, but there were many empty seats at the Liverpool end of the stadium.
Merseyside police, who attended the match as an observatory and adviser, said “the vast majority of the fans behaved in an exemplary manner, arriving at the turnstiles early and queuing according to instructions.”
“Their comments will be forwarded to the relevant authorities as part of the report on the game,” Deputy Chief of Police Chris Green said in a statement.
“We know that people will have witnessed many distressing scenes last night and we wish everyone a good trip home from Paris.
“Our aim today will be to support Liverpool City Council with the police of the parade back home.”
After the game, Liverpool coach Jurgen Klopp said the team was aware of pre-match incidents and that their families were affected.
“I haven’t been able to talk to my family yet, but I know the families had real struggles to get into the stadium,” he said.
“I heard some things that weren’t good. It was obviously pretty complicated, but I don’t know any more.”
Nigel Huddleston, the UK’s Minister for Sports, Tourism and Civil Society, tweeted that he was concerned about the “disturbing scenes” around the stadium and said his department “will work with the relevant authorities to find out what happen and why “.