With Arsenal finishing fifth during his only season at the north London club, Rioch was fired early into his second season and replaced with the legendary Frenchman.
"He was never going to last there," Dowson said of Rioch's time at Arsenal in an exclusive interview with Tribal Football.
"When Bruce Rioch came in he kind of ruined it to be honest. His dad was a sergeant major in the army and he tried to bring the army style into football, where it has no place.
Dowson started out his own playing career at Millwall, working under George Graham, John Docherty and Rioch.
Despite making just one league appearance for Millwall before his departure in 1991, Dowson built up a number of great relationships at the club and is still full of praise for Graham and Docherty.
"I had George Graham who ran by fear factor and you always knew what you were going to get," he said.
"Then I had John Docherty who was the best coach I ever played under and he signed me for three different clubs. Millwall was a special club when he was there."
Dowson is now the manager of National League side Woking, with his side currently ninth in the table and just a few points adrift of the playoffs.