Dawson lifted and dumped the former champion to the canvas, hurting his shoulder in the process.
Hopkins was unable to continue and referee Pat Russell awarded the victory to Dawson.
"I was backing up and he picked me up, both legs, and he threw me down with his shoulder and that's when it got hurt," Hopkins said.
"I told the referee I would continue with one arm but he stopped the fight. He never told me that if I stopped fighting, I would be disqualified.
"They set me up. Dawson was just in there to rough me up. That was a blatant foul and it should be no contest, not a disqualification."
It was the first technical knock-out registered against Hopkins in what was the 46-year-old's 61st fight.