According to Wood, Browns safety T.J. Ward yelled, "Hey, I told you to warn [Manuel] that we were going to get him!" toward Bills linebacker Kiko Alonso, who was a college teammate of Ward's at Oregon.
Ward on Friday denied making the comment.
"That is completely inaccurate. I talked to Kiko, we went to Oregon together. But any time a player gets hurt you never praise or root for a player to get hurt," Ward said. "There's never a reason for celebration."
Manuel left the game after the third-quarter hit, which came at the end of his scramble for a first down. Manuel has a lateral collateral ligament sprain in his right knee that will keep him out a few weeks, coach Doug Marrone said Friday.
"The hit was fine," Wood said. "What ticked me off was the way [the Browns] acted afterwards. I hope our defense never acts that way when they injure an opposing quarterback. You have to show some class in that situation."
Browns safety Tashaun Gipson delivered the hit on Manuel, who had just gained the necessary yardage for the first down and continued to run along the sideline. After the play, Gipson made a celebratory gesture in the direction of Manuel, who was grabbing for his right knee while on the ground.
"Maybe my gesture at the end probably didn't suit it well," Gipson said.
However, he defended his hit, responding "not at all" when asked if it was a dirty hit.
"It's the game of football. Things like that happen. I definitely don't intentionally try to hurt anybody. I wouldn't dare do that. I'm not that kind of player," Gipson said. "Our QB took a shot. Their QB took a shot. Not to say that we were trying to go one for one, but it's the game of football. He's running around on the sidelines. He could have gotten out of bounds. He didn't. So it's my job to bring the ballcarrier down."
The Browns lost their starting quarterback, Brian Hoyer, to a knee injury in the first quarter -- the team announced Friday that Hoyer has a torn ACL -- but Wood said he did not believe Gipson's hit was in retaliation for Hoyer getting hurt.
After the game, Marrone was defensive about Manuel's decision to continue running after gaining the first down.
"I don't think I'm ever going to, you know, tell someone not to score a touchdown," Marrone said. "You know, EJ's a tough kid. He took a shot. He scrambled. He made a first down. He's trying to score a touchdown. You know, what do you say? Don't scramble? Don't what? Don't score touchdowns? I mean, what do you think?"
When a reporter responded "go out of bounds," Marrone fired back.
"Go out of bounds? I'm sure he was working his way to the sideline," Marrone said.
Wood said Friday that Manuel may have gone too far in trying for extra yardage on the play.
"I know what he's thinking -- 'I'm going to do everything we can to get us down the field,'" Wood said. "He has to take less hits, though, and that was an unnecessary hit there."
Information from ESPN.com Browns reporter Pat McManamon was included in this report.