David Mueller said he was fired from his job at KYGO in Denver two days later - but claims one of his superiors committed the alleged assault.
Legal papers from Swift's lawyers show the singer solely accuses Mr Mueller.
She was said to be "surprised, upset, offended, and alarmed" he grabbed her bottom at a pre-show meet-and-greet.
"Mueller's newfound claim that he is the 'wrong guy' and, therefore, his termination from KYGO was unjustified, is specious," wrote Swift's lawyers in the legal documents.
"Ms Swift knows exactly who committed the assault - it was Mueller."
Swift's counterclaim comes after Mr Mueller sued her in US District Court in Denver in September. He said a member of the singer's security team had falsely accused him of groping her at the Pepsi Center on 2 June 2013.
However, Swift's lawyers added that Mr Mueller "did not merely brush his hand against the singer while posing for a photograph, but lifted up her skirt."
Her publicist released a statement shortly after she was sued by Mueller last month, saying the radio host's employer was given evidence after the incident and made its own decision to fire him.
Swift is requesting a jury trial and said any money she might receive from legal action would be donated to charities "dedicated to protecting women from similar acts of sexual assault and personal disregard."
Taylor Swift has filed a counterclaim against a US radio DJ who is suing the singer over allegations he groped her backstage at a concert in June 2013.