Adams, a fourth-year receiver, was taken to a local hospital after he took a helmet-to-helmet hit from Trevathan in the third quarter of Green Bay's 35-14 win at Lambeau Field on Thursday night.
The Packers said Adams was conscious and had feeling in all of his extremities. He gave a thumbs-up sign while he was being taken off the field on a gurney. He was being evaluated for head and neck injuries and the possibility of a concussion.
"I don't like anybody celebrating when a guy gets carted off the field," Packers quarterback Aaron Rodgers said. "That's kind of the message I was conveying to them."
Said Packers tight end Martellus Bennett: "What we thought was f---ed up was that he was celebrating that play. You get your ass kicked, you took a cheap shot and you celebrate when a guy goes down. That's what really pissed us off."
"I'm not a dirty player," Trevathan told reporters after the game. "So I don't do dirty hits."
An NFL spokesman said Friday morning that Trevathan's hit on Adams is being reviewed for potential discipline.
When Packers cornerback Davon House saw the replay on a reporter's phone after the game, he said: "Oh god, that's disgusting. That's illegal. I didn't see it like that [before]. Oh my goodness. That's dirty. I didn't see it like that. Yeah, that's dirty. I don't think we have any guys like that that would do anything malicious like that, but that is a dirty hit."
Officials penalized Trevathan for unnecessary roughness but did not eject him.
Referee John Hussey said after the game in a pool report conducted by ESPN that he "just didn't see enough to have it rise to that level [of an ejection]."
"He was being stood up; that's when 59 [Trevathan] came in, and what I felt was 59 came in and hit a defenseless player in the helmet area unnecessarily," Hussey said.
Trevathan said he planned to reach out to Adams.
"I regret the level I hit him at," Trevathan said. "But you got to understand, I had momentum, and I was just trying to make a play. ... Nothing intentional. It happens in this game."
Even though Trevathan was not ejected, he still could be subject to a suspension under league rules.
"I don't think it should be a suspension, but my main concern is that he's OK," Trevathan said.
"It was bad. I never wish that on nobody, especially after being hurt a couple times. I know how that is. Especially with the head and neck, you never wish that on nobody. You never want to see that, but this game is physical, and it happens. Hopefully, they can see my half of it."
Several Packers players, including Cobb, Nelson and Bennett, said they were planning to go right from the stadium to the hospital.
"The news that I was given on Davante, so far, everything looks positive," Packers coach Mike McCarthy said. "He's already giving them a hard time at the hospital to get out of there, so that's a great sign."
Nelson caught a 4-yard touchdown pass on the play after Adams was injured and went to one knee and bowed his head in the end zone amid a muted celebration from the crowd.
"That definitely was for Tae," Nelson said. "Obviously, we said some prayers while he was laying there. Just another opportunity to do it. It's not fun to see your brother like that laying there motionless like that, and being that close is scary. There's not enough prayers to be said."
Adams had two receptions for 13 yards and a touchdown before his injury.
ESPN's Jeff Dickerson contributed to this report.