"Wasn't handled the right way in our training room," Mayfield told reporters after a win over the Cincinnati Bengals.
Reports surfaced before the game that Beckham will require surgery on the injury at the end of the season. The three-time Pro Bowl receiver hasn't missed a game this year, but his production has dwindled.
"He's not able to run as well as he should be able to ... and that's frustrating for him," said Mayfield, who completed two passes to Beckham for 39 yards against the Bengals.
Beckham sustained the sports hernia during training camp. A surgical procedure at the time would have sidelined the 27-year-old early in the regular season but would likely have meant he'd be healthier down the stretch.
"I think it could've been addressed earlier on," Mayfield said.
"... He probably would've missed the first two (games), one or two. ... It's too late to do that. He's fighting through pain. He's playing through pain. That shows you what type of guy he is."
Mayfield tweeted a retraction after his comments picked up steam:
"My intentions were not to throw our medical staff under the bus," he wrote. "No I don't know all the facts about Odell's injury. It was emotionally answered because I can sense his frustration and I care about my team and putting us in the best position to win.
"Those people within our building know my intentions and where I am coming from. I truly believe that and I apologize to those that don't deserve the backlash.... today was a good team win. On to the next one."
Beckham declined to address the injury postgame or reports that he wants out of Cleveland.
"I'm not going to talk about any offseason stuff that's going on," he said, according to Scott Petrak of BrownsZone. "Right now the focus is to win, 1-0, and that's what we did today. Any other questions about it I'm not going to answer."