Davies has apologised to Cleverley, which has been accepted, for the challenge that left the midfielder sidelined for four weeks.
"I'm not really bothered about what any United fans are saying," he told the Manchester Evening News during a break in play at his annual Golf Day to raise funds for his Kids of Bolton charity.
"You put yourself on Twitter and you're out there - you've just got to ignore the people that are giving you grief.
"The referee dealt with it - there was no yellow card. I went to win the ball and it was a foul and unfortunately he got injured.
"But that's the game. It's a contact sport.
"When I was told Tom's injury was a suspected fracture I felt really bad.
"I've been a young player myself and he's broken into one of the best teams in the world and I was gutted for him. I texted him and he called me back five minutes later and said 'don't worry about it'. He accepted that it was a genuine attempt to win the ball.
"It's all done and dusted really and I've not heard anything since. Hopefully, he'll be back playing in three or four weeks."