The Sale Sharks owner made his offer almost two weeks ago and had urged administrators to speed up the process.
"I'm disappointed but not surprised by this outcome," he told BBC Scotland.
"I always said that I would only get involved for the good of the club and it seems my bid just wasn't good enough."
Kennedy was one of five interested parties aiming to succeed current owner Craig Whyte.
Former Rangers director Paul Murray's Blue Knights consortium, United States-based Club 9 Sports, a UK-based consortium and a Singapore-based consortium have all expressed an interest.
Administrators Duff and Phelps want a new owner in place by the summer.
Kennedy added: "I'm glad the process is moving forward and I just hope the administrators go with Paul Murray and his Blue Knights now.
"I think they have the best interests of the club at heart."
"I'm disappointed but not surprised by this outcome," he told BBC Scotland.
"I always said that I would only get involved for the good of the club and it seems my bid just wasn't good enough."
Kennedy was one of five interested parties aiming to succeed current owner Craig Whyte.
Former Rangers director Paul Murray's Blue Knights consortium, United States-based Club 9 Sports, a UK-based consortium and a Singapore-based consortium have all expressed an interest.
Administrators Duff and Phelps want a new owner in place by the summer.
Kennedy added: "I'm glad the process is moving forward and I just hope the administrators go with Paul Murray and his Blue Knights now.
"I think they have the best interests of the club at heart."
