With Parsons leading the charge, Dallas sacked Jones seven times and constantly pressured the New York quarterback in Sunday night's 40-0 blowout.
But despite the lopsided score and their inability to handle the Cowboys' pass rush, the Giants kept Jones in the game until their final possession -- a decision that drew widespread criticism.
"It's called protecting your guy -- something I thought the Giants should have done," Parsons said Tuesday on his "The Edge with Micah Parsons" podcast. "I don't think Daniel Jones should have been in that game in the fourth quarter.
"I thought they should have protected him and pulled him out. Barring injury, their season would be over without Daniel Jones."
Jones struggled in his first regular-season game since signing a four-year, $160 million deal in March. He completed just 15 of 28 passes and had two passes intercepted while being harassed throughout by the Cowboys, who pressured Jones on 55% of his 42 dropbacks.
Parsons had an upfront view of the wreckage; the two-time Pro Bowl pass rusher had a sack, a tackle for a loss and two other hits on Jones. It was the worst season-opening loss in franchise history, and fans at MetLife Stadium booed the Giants loudly as they exited the field at halftime with a 26-0 deficit. The second half wasn't any better for New York, which pulled multiple other starters -- including star running back Saquon Barkley -- despite leaving Jones in the game.
"I do not agree with Daniel Jones staying out there until that last drive, I thought that was wrong," Parsons said. "I thought that was deceiving.
"That's your franchise quarterback, and he's out there with a backup offensive line still getting sacked and hit. I just didn't understand. Maybe it was a prove-it moment by the Giants -- I have no idea -- a learning lesson, who knows. But I thought Daniel Jones should have got pulled out."
Coach Brian Daboll, when asked Sunday why Jones remained in the game with the outcome already decided, said New York simply was trying "to get something positive going." Jones also emphasized he "wanted to stay in" the game and said there "wasn't any conversation" about removing him.
"The Bengals [made] the smart decision by pulling Joe Burrow, saying, 'Hey, we're going to submit, we're going to take our loss, and we're going to move on to next week and get better,'" the two-time All-Pro said. "That's the best thing you can do."