The Premier League side said on Thursday that they would formally raise their concerns with UEFA, the host club and French police over the "unnecessary and disproportionate" force their fans were subjected to.
"Plans were in place to move 500 supporters at a time... once the first group of supporters was released, the police began using unnecessary and disproportionate force to stop the remainder of our fans from moving any further," Newcastle said in a statement.
"This was actioned through a combination of pepper spray, batons and shields, with numerous supporters being indiscriminately assaulted by the police.
"Many supporters were visibly distressed, particularly in the upper concourse area of the away sector, where crushing became apparent."
There was no immediate comment from the French police, Olympique Marseille or UEFA when contacted by Reuters.
Fans leaving the stadium shared their anger and frustration with Newcastle staff, the club added.
"We will be calling on UEFA, Olympique de Marseille and local authorities to formally investigate this matter to ensure lessons are learned and this behaviour is not repeated," Newcastle said.
"We are continuing to liaise with the United Kingdom Football Policing Unit (UKFPU) as we gather evidence on behalf of our supporters."
Newcastle are 11th in the Champions League, with nine points from five matches. They will visit Bayer Leverkusen on December 10.