Browns quarterback Manziel injured his hamstring in the first half and did not return as the Panthers won 17-13 in NFL action on Sunday.
Manziel's exit from the field with less than two minutes remaining in the first half was greeted by cheers at the Bank of America Stadium in uptown Charlotte, North Carolina.
The reaction of some fans angered Newton, who was involved in a car accident on December 9 that left him with two fractures in his lower back.
"The only thing I can say is it was sad to see the crowd's response when he was getting hurt, man," said Newton.
"I just think it was classless at that time. Anytime a person is hurt, you don't celebrate. I've had that done in my career. It takes the integrity out of the game.''
Manziel was hit by Panthers safety Colin Jones in the second quarter, which led to his early departure down the tunnel.
The 22-year-old completed three of eight passes for 32 yards before succumbing to injury.
"As I kept walking more and more, it just felt like something I hadn't experienced before," said Manziel. "I figured I needed to get checked out. Pretty frustrating."