The Premier League club said in a statement on Wednesday that they were looking into the allegations.
"Following detailed and troubling accounts given by Liverpool supporters attending the match against Sevilla last night, the club is seeking to establish the facts regarding their treatment at the hands of the host stewards and local police force," the Merseyside club said.
"The safety and security of our supporters is our paramount concern and we intend to gather all the relevant information before responding further."
SOS chairman Jay Mckenna said some members were refused entry to the ground because the flag they were carrying had the word 'defiance' written on it.
"What is more concerning is the reports of heavy-handed treatment of supporters, including physical assaults, with one committee member reporting she was punched as she was pushed out of the ground," SOS said in a statement.
A Sevilla spokesman told Reuters: "(The stewards) are not Sevilla employees. In any case, the security tell us that at the entrances three English policemen, including their security coordinator, Liverpool's director of security and seven security assistants were present and in no case was there any complaint or reason for one, with access to the stadium and the time in the stands passing without incident."
European soccer's governing body UEFA said it was aware of some issues at entrances used by Liverpool supporters.
Liverpool drew the Group E game 3-3 after losing a three-goal lead at Sevilla's Ramon Sanchez-Pizjuan stadium, leaving both teams still battling for a place in the last 16.
(Reporting by Martyn Herman; additional reporting by Rik Sharma in Madrid; Editing by Ken Ferris)
