Tor claimed that the FBI was "outsourcing police work" and paid the university "at least $1m (Â£675,000)".
Tor is a so-called dark net - a hidden part of the internet that cannot be reached via traditional search engines.
A university spokesman told the BBC: "You can read what you want into it."
The anonymised system lets people use the web without revealing who or where they are.
There are sites on it that offer legitimate content, services and goods but it also has a reputation for hosting criminal activities such as the selling of drugs and images of child abuse.
It gained notoriety in late 2014 when a big operation carried out by the FBI took down dozens of Tor sites, including the Silk Road 2, which was one of the world's largest online drug-selling sites.
It was this attack that the Tor Project is claiming was undertaken by researchers at Carnegie Mellon, which is based in Pittsburgh.
"This attack sets a troubling precedent," the Tor Project wrote  in its official blog.
"Civil liberties are under attack if law enforcement believes it can circumvent the rules of evidence by outsourcing police work to universities," it added.
Prof Alan Woodward, a computer science expert from the University of Surrey, said that such partnerships were not unusual.
"Universities work with law enforcement agencies all the time," he told the BBC.
"Were they paid $1m? I can't say but law enforcement agencies do sponsor research into ways to track criminals so it is not that surprising.
"The big difference in this case seems that researchers were asked to unmask a specific set of people and provide their IP addresses.
"I'd be more surprised if they did that as all universities have ethics committees so the big question is was there ethical oversight?"
Anonymity network Tor, notorious for illegal activity, has claimed that researchers at US Carnegie Mellon university were paid by the FBI to launch an attack on them.