Oldham said death threats received by staff, sponsors, and fans during a week of intense scrutiny on the third-division club made it impossible to sign Evans.
Evans criticized those who stopped his "lawful quest" to return to professional soccer.
"Sadly the 'mob rule' tactics employed by the more radical elements of our society and the constant media reporting has had the desired influence on some sponsors and the club would face significant financial pressure if I joined them," Evans said on his personal website.
Evans said funding for a new stand at Oldham's stadium would have been jeopardized if he played for the team.
"It would mean that workers would lose their jobs and others would be put at risk," he said. "That would simply not be fair."
The former Manchester City, Sheffield United and Wales striker maintains he was wrongly convicted of raping a 19-year-old woman in a hotel room in Wales in 2011. He was released from jail about three months ago and has since been trying to sign with a professional soccer team, while seeking to get his conviction overturned by the Criminal Cases Review Commission.
"Whilst I continue to maintain my innocence, I wish to make it clear that I wholeheartedly apologize for the effects that night in Rhyl has had on many people, not least the woman concerned," Evans said.
Several people have been fined for revealing the victim's identity online, and she has reportedly had to change her name several times and move.
"It has been claimed that those using social media in an abusive and vindictive way towards this woman are supporters of mine," Evans said. "I wish to make it clear that these people are not my supporters, and I condemn their actions entirely."
Oldham has lost sponsorship deals this week over its pursuit of Evans, and also said it received a "barrage of abuse."
"Proceeding could have placed significant financial pressure on the club and continued to be a divisive influence," Oldham chief executive Neil Joy said.
"We deplore and condemn the vile and abusive threats, some including death threats, which have been made to our fans, sponsors and staff whilst this process has been in the public domain," Joy added outside the club's stadium.
The Professional Footballers' Association is still helping the 26-year-old Evans find a team.
PFA chief executive Gordon Taylor compared Evans' bid to clear his name with Hillsborough stadium disaster campaigners who fought to ensure the 96 dead Liverpool fans were not blamed for the 1989 crush.
"(Evans) wouldn't be the first person or persons to have been found guilty, maintained their innocence, and then been proved right," Taylor told the BBC. "We know what was alleged to have happened at Hillsborough and it's now unravelling, and we're finding it was very different to how it was portrayed at the time — indeed by the police."
Rob Harris can be followed at www.twitter.com/RobHarris