"There will be absolutely no change with coach McCarthy," Jones told 105.3 The Fan. "I am surprised someone would question these unprecedented situations that everybody's been in.
"On top of that, no one's making excuses, but we've had some challenges in the injury category. If you look at his track record, and his pedigree, he's consistently won year in and year out. We have the utmost confidence this ship is going to be righted quickly."
The Cowboys (4-9) sit in last place in the NFC East. They hired McCarthy in January after firing coach Jason Garrett.
McCarthy, 57, had a 125-77-2 record in 13 seasons as Green Bay Packers coach from 2006 through 2018 before he was fired. He won a Super Bowl with the Packers in 2011. He did not not coach in 2019.
Dallas began the season with a 2-3 record before it lost starting quarterback Dak Prescott to a season-ending ankle injury.
The Cowboys have won just two of eight games since Prescott's injury. They have allowed a league-high 30.8 points per game and 162.7 rushing yards per game.
"Mike's going to be the leader of this group," Jones said. "He's, certainly, a great head coach. I think we're going to see that going forward. He's accomplished a lot, and he's going to accomplish a lot more before it's all said and done."
The Cowboys will host the San Francisco 49ers at 1 p.m. EST Sunday in Arlington, Texas.