Perkins suffered the injury on punt coverage in the first quarter, and he was carted off with a large cast immobilizing his entire left leg.
Clawson had been hoping to visit Perkins for several days but couldn't because the Syracuse senior had been in intensive care at Wake Forest's Baptist Medical Center.
Syracuse on Wednesday said Perkins is out of ICU, and is still hospitalized. The university is "hopeful" Perkins can be transported back to Syracuse this week once he is cleared to travel.
"You go down your senior year to play a football game and you're playing. Next thing you know, you're in a hospital in a strange town, and your teammates and your coaches aren't there," Clawson said Wednesday on the ACC coaches' teleconference. "We had a player last year that had a similar injury, and I know how tough it is.
"I just wanted to go over and let him know that there's people here that care about him. Even the player of ours that had that injury last year, I think, reached out to him. It's part of football, but it's hard to ever see a young man suffer that type of injury and then not be able to be with his teammates for a couple of days."
Clawson wanted to visit Perkins before Wake Forest left for Thursday night's game at NC State. Perkins sent a picture of he and Clawson to Syracuse coach Dino Babers after the visit.
"That was something that was very gracious on his end," Babers said of Clawson. "For him to go out and visit one of my guys in the local hospital is something I'll never forget; something that I'll always appreciate."
Clawson said Perkins' surgeons did a good job and that the prognosis is promising. Perkins, a native of Glen Head, New York, has played on both sides of the ball but has been used primarily on special teams during his Syracuse career.
"He knows what's ahead, but I think he also knows it could have been worse," Clawson said. "Given everything that happened, he's in a really good place. He was a very mature young man, appreciative of how he was treated and the treatment he got, and just had a great attitude. I was really impressed with him."