The Reds lost to Real Madrid 1-0 at the Stade de France, just north of the city, on Saturday evening.
However, shambolic scenes outside the ground saw supporters with tickets made to wait in huge queues, before French police used tear gas.
Some were kept out of the stadium for large swathes of the first half and fans spoke of officers pointing guns at them after the game.
Liverpool defender Andy Robertson said it had “not been well organised”, adding that many of the players’ families and friends were caught up in the scenes.
Cabinet minister said it appeared French officers used an “aggressive approach”, while a UK police force defended the “exemplary” behaviour of fans.
Supporter Greg Scott, said his experience had been “shocking”.
He told PA: “I’ve travelled to many stadiums around Europe, away days, that kind of thing.
“But never have I seen anything like this, complete lack of control from the police.
“Their excuses stink – it’s nothing to do with the fans, the club, it’s (organisers) Uefa and the French police.
“People could have been seriously hurt, we were piled in together for hours in the heat queuing up, and then we had no idea where to go next.
“French police were using tear gas on a calm crowd like it was nothing, those with tickets were kept outside, I didn’t see most of the first half.”
Another told of being in “fear” of the French police.
Supporter Robbie, 24, who did not want to give his surname, said: “I got pepper-sprayed, the first time that’s ever happened to me.
“It was unprovoked, people were just standing there waving at the police to let us in, we had tickets.
“Police were just spraying us for no reason, even kids and older people, it was bad.”
Liverpool FC supporters union Spirit of Shankly said on Twitter on Sunday: “Last night was totally shambolic and extremely dangerous- we are gathering evidence from fans.”
The issues started hours before the game, as tens of thousands of Liverpool fans were funnelled underneath a bridge close to the stadium, where they waited for hours in long queues.
#CLFINAL @LFCHELP @SPIRITOFSHANKLY
MERPOL was deployed to this evenings match. Can only describe it as the worst European match I've ever worked or experienced. I thought the behaviour of the fans at the turnstiles was exemplary in shocking circumstances. You were not late 100%
— MerPol Liverpool FC (@MerPolLFC) May 28, 2022
Footage on social media appeared to show people climbing over barriers as crowds built up, and the kick-off was delayed by more than 30 minutes.
Police carrying shields and riot gear moved into the area shortly after 8pm and began using tear gas.
Tensions outside the stadium were then driven by young Parisians, causing ticket gates to be shut.
Bottles were thrown at officers who responded with tear gas.
Supporters argued with ticket officials on the other side of the fence after being refused entry.
Beyond the gates some people, a few wearing Liverpool shirts, were taken away.
Those with tickets were later let into the stadium well after the match began.
Similar scenes also took place at the fan zone in the Cours de Vincennes area in the south east of the city.
Police said 68 people were arrested and a nearby pub of 500 football fans was evacuated.
Northern Ireland Secretary Brandon Lewis told Sky News’s Sophy Ridge On Sunday programme: “I think it is concerning, I think we do need to ensure that they are looking into how this happened.”
He added: “We’ve got to learn a little bit about what happened over there, get to the bottom of it.
“But it is concerning to see that people either didn’t get into the stadium or were treated in the way that some of them seem to have been treated, with a very aggressive approach.”
Uefa said the delay was caused by the late arrival of Liverpool fans, but the club said that was “totally inaccurate”.
A Merseyside Police spokesperson said: “Can only describe it as the worst European match I’ve ever worked or experienced.
“I thought the behaviour of the fans at the turnstiles was exemplary in shocking circumstances.
“You were not late 100%.”
A statement from Prefecture de Police, the Parisian police force, said queues formed after fans arrived without tickets.
French minister of sport Amelie Oudea-Castera, who attended the game alongside French interior minister Gerald Darmanin, wrote on Twitter: “The attempts of intrusion and fraud by thousands of English fans have complicated the work of stewards and police forces but will not tarnish (Real Madrid’s) victory.
“Violence has no place in the stadiums.”
It is understood the UK ambassador to France has contacted the French Ministry of Interior directly urging an investigation.
Uefa said turnstiles were blocked because some Liverpool fans had purchased “fake” tickets, leading to a build-up.
Liverpool later released a statement calling for a thorough investigation into events outside the ground.
Culture Secretary Nadine Dorries said the footage circulating of the scenes was “deeply concerning” and suggested Uefa launch a formal investigation.
“I urge UEFA to launch a formal investigation into what went wrong and why, in coordination with stadium staff, the French Police, Federation Francaise de Football, Merseyside Police and Liverpool Football Club,” she said in a statement.
Sports minister Nigel Huddleston tweeted that the Department for Culture, Media and Sport (DCMS) “shall be working with the appropriate authorities” to find out what happened.
It is understood that the DCMS will be contacting Uefa about the matter.
A Foreign Office spokesperson said: “Our consular staff are supporting individuals who have been affected by the events in Paris, and are in touch with local authorities.”