Liverpool have called on Uefa to "fully and transparently" implement the recommendations made in an independent report on the events before last season's Champions League final.
Fans were penned in and teargassed outside Stade de France in Paris before the match between Liverpool and Real Madrid on 28 May 2022.
The report ruled Uefa bore "primary responsibility" for the chaotic scenes, adding it was "remarkable" no-one died.
Liverpool said "positive and transparent action" must be taken "to ensure there are no more 'near misses'".
The club added the "fundamental safety failings" had "exacerbated the suffering" of the families, friends and survivors of Hillsborough.
"We implore Uefa to fully enact the recommendations as outlined by the panel - no matter how difficult - to ensure supporter safety is the number one priority at the heart of every Uefa football fixture," Liverpool said.
The report - commissioned by Uefa three days after the final which Liverpool lost 1-0 - made 21 recommendations in an attempt to ensure "everything possible is done" to prevent a similar incident happening at a major sporting event.
It also warned French authorities this should be a "wake-up call" before it hosts the 2023 Rugby World Cup and 2024 Olympic and Paralympic Games.
'Shocking false narratives' after 'disaster' final
Uefa and French authorities initially blamed ticketless Liverpool fans for the events, but the report - released on Monday - said there was "no evidence" to support the "reprehensible" claims.
It added the collective action of Liverpool supporters was "probably instrumental" in preventing "more serious injuries and deaths" outside the stadium.
"Shocking false narratives were peddled in the immediate aftermath of that night in Paris; narratives that have since been totally disproven," said Liverpool.
"The independent French Senate report published in July 2022 found Liverpool supporters were unfairly and wrongly blamed for the chaotic scenes to divert attention from the real organisational failures.
"The Independent Senate report also published 15 recommendations for improvements. No action has been taken on these recommendations to date."
For many Liverpool fans, the incident and subsequent attempted attribution of blame on supporters evoked painful memories of the Hillsborough disaster.
Ninety-seven Liverpool supporters died as a result of the April 1989 disaster at Sheffield Wednesday's stadium, where fans were crushed because of overcrowding in the Leppings Lane end at an FA Cup semi-final against Nottingham Forest.
"It is shocking that more than 30 years after the Hillsborough disaster any club and our group of fans would be subject to such fundamental safety failings which have had such a devastating impact on so many," the club added.
"But even more concerning is the realisation that for families, friends and survivors of Hillsborough, Paris has only exacerbated their suffering.
"Our thoughts go out to all our fans who have suffered as a result of Paris and we would remind them of the mental health support we put in place in the days following the disaster that was the Uefa Champions League final in Paris."
