Anton, 20, and three team-mates from Brighton and Hove Albion were found not guilty of sexual assault and voyeurism.
The retrial at the Old Bailey followed an earlier trial in which a jury could not agree verdicts.
Mr Rodgers said: "The last 18 months have been extremely traumatic for us as a family, but we are relieved that Anton's name has been cleared.
"I am also pleased for the other defendants and their families, that they can now get on with living their lives without these hurtful allegations hanging over them."
He thanked Liverpool FC and its fans for their support "through this distressing process".
Mr Rodgers and his wife had sat through the two trials with the families of the other defendants.
Anton Rodgers, Lewis Dunk, 21, and George Barker, 21, and former team-mate Steve Cook, 22, who now plays for Bournemouth, had maintained their innocence.
They broke down and were visibly shaken as they were consoled by their girlfriends and family outside the court.
Anton's solicitor Mark Haslam said: "We are delighted the jury has reached the correct verdict in this case.
"The last 18 months have been very stressful for Anton and his family, so it is a great relief that this long ordeal is finally over."
Barker said: "Since the day of my arrest in January 2011, I have always vigorously protested my innocence.
"Having to live with these allegations over the last two years has been enormously difficult for me, for my family and for my friends.
"Being able to rely on them at all times has been hugely reassuring during what has seemed at times like a nightmare.
"I am now looking forward to spending some time with my family and getting on with my life and my football."
Cook left court with his family without commenting.
Dunk said: "This is the best feeling in the world."
His father Mark added: "I believed 100% that he was innocent and now it has been proved in court.
"I hope he will be able to build up his career again. This sort of thing would have an effect on anybody's career."
Dunk's solicitor Steven Barker said: "Lewis is looking forward to putting the ordeal of being wrongly accused of these matters behind him and regaining his place in the Brighton first team."
The prosecution said the players were celebrating victory in a local cup in July 2011, when they came across the drunken woman at a club.
She woke up at the Jury's Inn hotel to find her strapless dress pulled down and said she saw explicit pictures on Rodgers' mobile phone.
Richard Barton, prosecuting, said these were taken as a "permanent record of their conquest".
But despite forensic tests on all the players' phones, only one photograph was found on Barker's phone.
It showed the sleeping woman with shaving foam spelling out GB on her thigh. Barker was next to her doing a thumbs-up sign and smiling.
Another player, Leon Redwood, said he went into the room at night and sprayed the foam.
Barker and Rodgers said the woman had joined in the "boy's banter". She climbed into bed with them and started kissing them.
Dunk and Cook said they were sleeping on the floor and did not get involved with the woman.
The 19-year-old woman was said to have "told a pack of lies" following the incident.
She agreed she lied to police and her employers but said she had been humiliated by the sportsmen.
She complained to police about the players six months later after getting into a volatile relationship with another player, Kazenga LuaLua.
He wound her up about her photographs being shown around the club and kidded her that a video would be put on YouTube.
Police have been unable to find anyone at the club who had seen pictures of the woman.
The woman said she was not drunk but her friend said they had each drunk between 10 and 15 shots of alcohol and shared a bottle of wine.
:: Brighton this week released Rodgers and his team-mate Ben Sampayo, who was a reluctant prosecution witness in the case.