McCarthy met with the media on Monday to discuss Sunday's game and the status of the All-Pro gunslinger.
"I didn't like the hit. It was totally unnecessary in my opinion," McCarthy said, according to the team website. "He's clearly expecting to get hit, and to pin him to the ground like that, I felt it was an illegal act.
"To sit here and lose any of your players to something like that, it doesn't feel good."
Rodgers suffered a broken right collarbone on the play. The hit occurred with 7:05 remaining in the first quarter. Rodgers took a snap on a second and nine and scrambled to his right, before dropping off a pass to Martellus Bennett.
Minnesota Vikings linebacker Anthony Barr hit Rodgers on the play, forcing the quarterback to land awkwardly on the ground. Rodgers landed directly on his right shoulder.
Vikings coach Mike Zimmer told reporters Monday that he did not speak to Barr about the hit.
"No, I haven't talked to him," Zimmer said. "I don't know what the scrutiny is. We're playing football. It's unfortunate that he got hurt but I think everything was above board. We're not a dirty football team. We'll never be a dirty football team as long as I'm here. We're going to play within the rules and sometimes things happen."
Meanwhile, the Packers signed quarterback Joe Callahan on Monday and will start Brett Hundley with Rodgers forced out of action.
Rodgers will have surgery and is likely out for the season. McCarthy has yet to announce if Rodgers will remain on the team's roster.