Allen is scheduled to undergo an MRI on Monday.
"It's hard," McCoy said. "Keenan has worked so hard to get where he is. Give him a lot of credit for what he's done and how hard he's worked."
Allen, 24, suffered the injury with just over two minutes left in the second quarter of the Chargers' 33-27 overtime loss. His right knee appeared to buckle as he came out of a break and he fell to the ground. Teammates gave Allen a hug as he was carted off.
"He was pretty emotional," said tight end Antonio Gates, one of Allen's closest friends on the team. "I just told him that I love him and that he's my hero. I know how bad he wanted to play this year, due to the circumstances of what he had to deal with last season.
"He did all of the necessary things this offseason. I watched him work during training camp. I pushed him to the max, and I expected him to be the best receiver in the NFL this year. Unfortunately, he's going to have to wait until next year."
Allen was having a good day, with six catches for 63 yards on seven targets in the first half.
"They couldn't cover him," Chargers quarterback Philip Rivers said. "And they knew they couldn't cover him. And then he goes down."
Allen had 67 catches for 725 yards and four touchdown catches last season through eight games and was well on his way to his second 1,000-yard season, but he suffered a kidney laceration in the eighth game and missed the rest of the season.
In June, Allen signed a four-year contract extension worth more than $44 million.