Jones played all but three offensive snaps in the Giants' 40-0 loss, despite playing behind backup offensive linemen late in the game. Tyrod Taylor came on with 1:10 remaining to take the final three snaps.
"It's called protecting your guy," Parsons said Tuesday on his podcast, "The Edge with Micah Parsons."
"I don't think Daniel Jones should have been in that game in the fourth quarter," Parsons said. "I thought they should have protected him and pulled him out. ... (Their) season would be over without Daniel Jones."
Parsons had one of the seven sacks on Jones, playing in his first game since signing a $160 million extension in March. Parsons also had two hits on Jones, who was pressured by the Cowboys on 55 percent of his 42 dropbacks, per ESPN.
Giants coach Brian Daboll said after Sunday's game that the team was just trying to get something going and that there was never a conversation about pulling Jones.
"I do not agree with Daniel Jones staying out there until that last drive," Parsons said. "I thought that was wrong. I thought it 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."
Jones and the Giants (0-1) return to action on Sunday against the host Arizona Cardinals (0-1). He finished 15-of-28 passing for 104 yards with two interceptions against Dallas.
—Field Level Media