A jury yesterday found pub bouncers Steven O'Rourke and James Hyndman not guilty of raping the woman, who cannot be identified for legal reasons.
Co-accused Robert Miller and Ryan Dunn had earlier been cleared of the same charge after the Crown decided to drop proceedings against them midway through the trial.
Outside court, Mr Dunn said: "It is completely unfair that we have all been named and been made out to be animals when it was all a pack of lies.
"She is just an attention-seeker and she should be named and shamed for what she has done to us. It has ruined our lives."
Edinburgh South Liberal Democrat MSP Mike Pringle said the men had suffered "a travesty of justice" and backed their calls for a change in the law.
He said "I see no reason why that woman should not be named. I think these men have every right to say that either their names should have been kept sub-judice or all parties' names should be disclosed.
"I'm in favour of everyone being completely anonymous until they are found guilty and if they are found not guilty, their names should not be disclosed.
"People say mud sticks and I have every sympathy with these four young men. She obviously falsely accused them and people should know she is a liar."
The woman, from Bathgate, claimed she had been gang-raped by four men at her former home in the town on 11 February and that they had threatened to kill her.
But the jury preferred the men's account of the evening – that she had simply invited them all back to her home and then willingly engaged in group sex with three of them.
The High Court in Perth had heard how the woman had put on her red lace underwear and gone out on a solo pub crawl which ended in the Livery Lounge bar.
Shortly after entering the bar, she invited the four men back to her flat to "party" and was "having a laugh and a joke" about group sex on the way home.
O'Rourke, 24, Hyndman and Dunn openly admitted having sex with her, while Miller was banished to another room when she said she would "do three, but not four".
Mr Dunn revealed that the group sex had ended when the woman became concerned about her kitten. He said the change in atmosphere led to the gang throwing items out of the fourth-floor window.
"Our behaviour was appalling then and we shouldn't have done that but we never raped her."
Lothians SNP MSP Ian McKee said on balance he supported anonymity for rape accused. "If the person making the accusations is being protected, it would seem reasonable the person accused should have their name withheld until the case is over."
But Linlithgow Labour MSP Mary Mulligan said she was against any change in the law.
She said: "There are no other cases, even murder, where an accused's identity is withheld and I don't see why this should be any different. I believe a woman needs to be protected in these circumstances."
Livingston SNP MSP Angela Constance added: "I would not support the woman being named because it may discourage genuine victims from pursuing cases."