Cox and captain Callum Mills fronted the media in Sydney on Friday morning, speaking publicly for the first time since five Swans players were suspended for the rest of the season for "breaching club standards".
There are ongoing allegations that more than the five players - Isaac Heeney, Chad Warner, Nick Blakey, Riley Bice and James Jordon - were in the room at East Melbourne's Pullman Hotel early on Monday morning.
A lawyer acting for two women of the three alleged victims at the centre of the investigation has claimed there were "more than five" men in the room, but declined to answer whether any coaches were present.
"I cannot comment on what happened in the room. It is a police investigation," Cox said before adding he was not in the room.
The Swans later issued a statement saying only the five players reported were in the room and condemned "misinformation" being circulated.
"We have every reason to consider that reports to the contrary are simply false," the statement said.
"We are respecting the process with the relevant authorities and will refrain from commenting on police matters.
"We would also like to take this opportunity to condemn some of the misinformation being reported and are now considering our legal position on those matters."
Cox was out himself well after midnight celebrating Sydney clinching a top-two spot and two home finals with a 36-point win over Essendon on Sunday.
But he was coy when asked if it was a mistake to give his players a free pass to go out drinking without a curfew.
"We spoke about post-game, about what's required to make the right decisions," Cox said.
"These obviously aren't the right decisions and that's why we've acted as a football club and come down with the sanctions."
Asked how much soul searching he'd personally done this week, Cox said: "It's been a really hard week for everyone involved at the football club. We're not shying away from that".
Cox conceded he and other "leaders" within the club needed to take responsibility in rebuilding the Swans' battered reputation after the lawyer claimed the two women involved were treated to "abhorrent" actions, the worst he'd heard of in 28 years.
"I've been at the football club for nine years. Every person within those four walls we value extremely highly and they have a massive say on our culture as a group," he said.
"We understand as leaders we need to lead that culture, but what we are going to do is back ourselves, and we're going to move forward and we're going to strive as strongly as we possibly can to repay the faith."
When handing down the club's punishment on Wednesday, Swans chairman Andrew Pridham said the sanctions would "torpedo" the second-placed Swans' premiership hopes.
Already there are claims there is a massive dressing-room divide with just one home-and-away round left to play before the finals and the five banned stars may have played their last games for the club.
But Mills denied there was a "rift" within the playing group.
"We just take every day in its stride," he said.
"Everyone's going to be feeling every different emotion, but we'll work together and we'll stay together.
"Football's secondary at the moment, but we will stick together."
Independent of the AFL-endorsed club bans, Victoria Police Sex Crimes Squad detectives have flown to Sydney to continue the investigation into Monday morning's activities.
No charges have been laid and AAP is not suggesting any wrongdoing.
