Romo looked to be on his way to the best performance of his career to date when he threw for a franchise-record 506 yards and five touchdowns against the Denver Broncos on Sunday, but a late interception allowed the opponents to score a field goal to seal a dramatic 51-48 win.
However, Bryant insists that Romo has the backing of his side despite the mistake and praised the 33-year-old's ability to ignore criticism.
"In my eyes, Romo is a fighter. I don't think no quarterback in this league takes as much criticism as he takes, and he still goes out there and acts like he hasn't heard anything," Bryant told reporters.
"I know he heard it, but he don't let it get to him. He goes out there and performs the best way he possibly can, and we're going to forever back him."
The Cowboys' next match comes against the Washington Redskins on Sunday as they look to improve on their 2-3 record.