Shockey says he saw "about 10 players" who didn't do the traditional gesture when the anthem is played, and he told some of them how he felt during Carolina's 28-13 victory.
"I was pretty upset in the way they weren't showing respect to America during the national anthem," Shockey said. "This is America and you should at least give respect to America."
Shockey's rant came in response to a reporter's question about the Texans' defense.
"This is America and this is just a game and they should not only be very proud of this country, but very gifted to be living here," Shockey said. "Maybe they just forgot to do it or something, but I don't see how you could forget to do that."
When told of Shockey's comments, Texans linebacker DeMeco Ryans fired back at the Panthers tight end.
"If he's so patriotic, why was he looking at our bench instead of the flag?" Ryans said, according to the Houston Chronicle. "Where did he come up with the number 10? Was he counting? Why was he paying attention to us during the national anthem?"
Shockey sports a red, white and blue tattoo on his right biceps portraying a bald eagle draped in an American flag. He caught a 9-yard touchdown pass from Cam Newton in Sunday's game, then pointed at Ryans and appeared to yell at him and cornerback Jason Allen.
Information from The Associated Press was used in this report.