Per Matt Lombardo of NJ Advanced Media, Shurmur said Mayfield's remarks were "not original commentary."
"Some people overthink it," Mayfield said. "That's where people go wrong. They forget you've gotta win."
The Giants are spending a lot of this preseason answering questions about their offseason moves.
Odell Beckham Jr. told Sports Illustrated's Ben Baskin that New York's front office is "stuck in an older mindset" and they traded him to the Browns because "thought they'd send me here to die."
Asked about the comments coming from outside of the Giants locker room, Shurmur tried to brush it aside.
“Quite frankly, on our list of issues of the day, it really doesn’t matter what Odell or Baker say," the Giants coach said, via The Athletic's Dan Duggan.
New York's selection of Jones was the most-talked about choice in the 2019 NFL draft. The response was overwhelmingly negative from fans, who booed when the pick was made, and analysts felt it was one of the worst choices in the first round.
Shurmur called Mayfield "the latest in a long line of critics of that pick."
Jones has given New York hope for the future with a solid preseason. The former Duke star is 16-of-19 for 228 yards and two touchdowns in two games.
Shurmur and the Giants coaching staff remain committed to Eli Manning as their starting quarterback in the regular season. Jones won't be able to prove his skeptics wrong until the team gives him the reins.