Signal-caller Matt Cassel had become unpopular with fans while struggling as the Chiefs' quarterback since taking over the job in 2009.
Cassel was knocked out of Sunday's 9-6 loss to Baltimore in the fourth quarter when he suffered a head injury on simultaneous hits from two defenders.
Kansas City fans erupted in derisive cheers -- apparently over the prospect of his absence -- as he wobbled off the field under his own power, The Kansas City Star reported.
That angered Winston, who told reporters Monday the fans had crossed the line of decency.
"We are athletes. We are not gladiators," he told the newspaper. "This isn't the Roman Coliseum."
He acknowledged fans are entitled to express themselves, "but when you cheer somebody getting knocked out, I don't care who it is, and it just so happened to be Matt Cassel, it's sickening. It's 100 percent sickening.
"I've been in some rough times on some rough teams. I've never been so embarrassed in my life to play football than at that moment right there."