Liverpool fans outside the Stade de France before the Champions League final with Real Madrid
Liverpool fans described heavy-handed policing, organisational chaos and overcrowding at last Saturday's showpiece game.
Real Madrid have asked for answers on the "series of unfortunate events".
"No football fan should be put in that situation, and it must not happen again," said a Uefa statement.
"Uefa wishes to sincerely apologise to all spectators who had to experience or witness frightening and distressing events in the build-up to the Uefa Champions League final at the Stade de France on 28 May 2022 in Paris, on a night which should have been a celebration of European club football."
French president Emmanuel Macron said ticket holders who were blocked from entering the stadium by security staff must be reimbursed "as fast as possible".
Macron said: "I have a thought for the families who have been pushed around, who have not been able to access the seats they had paid for.
"I have asked the government to clarify what happened, to determine the responsibilities and to explain them in detail to our compatriots, the British and the Spanish."
European football's governing body had previously announced that an independent review of what happened in the build-up to the final, and what lessons should be learned, would be led by Dr Tiago Brandao Rodrigues from Portugal.
French authorities and Uefa had blamed late arrivals and fake tickets for chaotic scenes outside the Stade de France, which caused the match to be delayed by more than half an hour.
Police used tear gas and pepper spray on some fans. It has also emerged that supporters were targeted by local gangs.
France's interior minister, Gerald Darmanin, said only English fans had caused problems at the final.
"The review will seek to establish a full picture and timeline of what occurred during the day, both within the stadium and the surrounding areas, including examining spectator flows to the stadium via the various access points," added Uefa's statement.
Liverpool legend Sir Kenny Dalglish said the apology was "a start" but added: "There is still a long way to go.
"This apology doesn't cover the false message about the late kick off, events at the fan park, or what happened in the aftermath."
A message on the screen inside the Stade de France originally stated the "late arrival of fans" was to blame for the kick-off being delayed
Earlier on Friday, Real Madrid issued a statement asking for answers about "unfortunate events" at the game, which the Spanish team won 1-0.
They also want to know why the Stade de France was chosen for the game and who was "responsible for leaving the fans abandoned and defenceless".
"Football has transmitted an image to the world which is far away from the values and goals which it should pursue," said the statement.
Real Madrid cited "unfortunate events" which took place "in the surroundings of and at access points to the Stade de France, and even inside the stadium itself" and added their fans "fell victim to said events".
They added: "We would like to know the reasons which led to this venue being chosen to host the final and the criteria used, taking into account the experiences of the day.
"Furthermore, we call for answers and explanations in order to determine those responsible for leaving the fans abandoned and defenceless. Fans who in general terms showed exemplary conduct at all times.
"We believe something which should have been a wonderful festival of football for all fans who attended the game, quickly turned into a series of unfortunate events which have caused a sense of outrage around the world.
"As was evident in the revealing images published by the media, several fans were attacked, harassed, assaulted and robbed in violent fashion.
"These occurrences continued as they moved in their cars or buses, causing concern for their physical wellbeing. Certain fans even had to spend the night in hospital as a result of injuries."
The club added: "Our fans and supporters deserve a response and those responsible to be held accountable in order for events like these to be eradicated from football and sport in general."
On Thursday, Liverpool chief executive Billy Hogan called the comments by France's interior minister blaming English fans "disgraceful".
"My response to the French minister's comments again, as I said earlier in the week, is just one of disbelief frankly," added Hogan.
He said 6,500 fans had responded to a request by the Premier League club, asking supporters who attended the final to complete a feedback form in order to support any investigation into the operational management of the event.
"The pain, the grief, the harm, the hurt that [fans] suffered on Saturday, and now to be told by a French minister that only Liverpool fans have been a problem, it's just disgraceful," said Hogan.
"We've written to Uefa again and we've raised specific questions - 13 specific questions - that we'd like them to clarify around the details of this investigation," said Hogan.
"We just feel it's incredibly important that we get this investigation going, frankly that we get it launched immediately."
-- Courtesy of BBC Sport