"Why would you risk losing your best player, your franchise's more important piece in a game that was already lost?" Jones wrote.
Coach Dirk Koetter defended the decision in his postgame press conference.
"Some of you may not understand this, but the captain always wants to go down with the ship," he said. "That's how it is, and Jameis is that kind of guy."
Winston confirmed he did not want to come out of the game.
"I'm here to play," he said. "I play football for a living. I'm going to be out there on the field with my brothers fighting until the end."
Count ESPN's Mike Greenberg among those who agree with Jones that Koetter should have pulled Winston from the game.
"In my opinion, to put a young franchise quarterback on the field down 33 points with one minute left in a game is not a smart decision," Greenberg said Monday morning during his "Mike & Mike" radio show with Mike Golic.
Golic disagreed, arguing that if a quarterback is playing poorly, he should stay on the field with his teammates until the end of the game.
"You go down on the ship with your guys," he said. "You're the leader of that team. You might not think there's anything to it, Greeny, but there's a ton to it. It means something to players on the field who are playing."
Greenberg countered that even if Winston wants to stay in the game, it's Koetter's responsibility — for the sake of the franchise — to remove him and avoid risking injury.
"The coach is the one who's got to say, 'You know what, guys? We're going to come back and fight another day here, and this guy is my franchise. I'm not putting him out there,'" he said. "You just fired your previous coach because the single most important thing in the franchise is to develop Jameis Winston. So I get leaving him out there at the beginning of the fourth quarter even though the game was hopelessly lost, but one last drive at the end of the game?"
To leave Winston in the game at that point was insane, Greenberg said.
Later in the show, the hosts posed the question to Donovan McNabb, the former Eagles, Washington and Vikings quarterback. McNabb explained that while a struggling quarterback might want to stay in the game until he can find a rhythm and execute some positive plays, the wisest move is to take him out.
"Look at all the quarterbacks going down right now," he said. "Imagine if Jameis Winston ends up getting hurt in that game. … This is the face of your franchise. They haven't had a true face of their franchise in over a decade."
Winston's teammates respect him, McNabb said, so even if he had come out of the game late, "I don't think anyone would have turned their back on him."
To listen to Greenberg and Golic scream at each other, click here.
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Contact Thomas Bassinger at email@example.com. Follow @tometrics.