"He'll just continue to get better," Fox said, according to the team's Twitter page.
Tebow overcame lots of ragged moments by throwing two touchdown passes in the final 2:44 of regulation to help the Broncos beat the winless Dolphins in overtime, 18-15.
"I liked the last 5 minutes more than the first 55," Fox said Monday.
Tebow started for the benched Kyle Orton, and through much of the game the Broncos sputtered. Tebow was sacked seven times as he struggled to identify blitzes, and several throws landed nowhere near a receiver.
The Broncos appeared beaten when they trailed 15-0 with 5:23 left and took over at their 20. At that point Tebow was 4 for 14 for 40 yards, and Denver was 0 for 10 on third-down conversions.
"It's my fault that we were in that position in the first place," Tebow said Sunday. "I just have to play better in the first three quarters so we don't have to make that comeback."
In the frantic final minutes of the fourth quarter, Tebow led TD drives of 80 and 56 yards sandwiched around a successful onside kick. He scored a 2-point conversion standing up with 17 seconds left to tie the game.
The Broncos (2-4) became the first to rally from a deficit of at least 15 points in the final three minutes since at least 1983, according to STATS LLC. Miami (0-6) extended the NFL's longest losing streak to nine games, leaving the status of embattled Dolphins coach Tony Sparano even more tenuous.
Fox said he thought Tebow handled starting for the first time this season "very well."
"I think that'll just get better as he develops more confidence in the (offense and his teammates)," Fox said.
Information from The Associated Press was used in this report.