Tebow played the balance of the game, a 31-22 victory for the Patriots, finishing 4-for-12 with 55 passing yards to go along with 31 rushing yards on four carries.
"I think I've got room for improvement," he said after the game. "I did some things well, there are some other things I'd like to do better, and I think that's what these games are for. I definitely want to learn from it and improve and next week do a little bit better."
Tebow, who has been working as the team's third-string quarterback, was 0-for-2 on his first drive before being sacked on third down, leading to a punt. He led one scoring drive, with running back LeGarrette Blount rushing for a 1-yard touchdown on the team's first possession of the second half.
"It felt good, just playing the game that we all love, it's a lot of fun," he said. "It felt really good."
The Patriots showcased a different offensive approach for stretches with Tebow in the game than they normally operate in with regular starter Tom Brady on the field, relying on several designed runs and read options.
"It's fun, and I'm definitely comfortable [with the read option]," Tebow said. "It's something I've done a lot. With that there's a lot of moving parts and you have to get those down, and that's something that we're still working on."
Patriots coach Bill Belichick lumped Tebow's performance in with the rest of the players during his postgame remarks.
"Really, I think it's all about the same for everybody," he said when asked to assess Tebow's performance. "We did some good things out there; it was far from perfect. We can all learn from it. We're going to learn from it, and we'll all improve."
The 25-year-old Tebow has shown steady growth throughout training camp as he hopes to cement a spot on the team's 53-man roster. The Patriots have kept just two quarterbacks on their active roster in three of the past four seasons.
Though Tebow has been seen on some of the Patriots' scout teams during special-teams drills, he's worked exclusively at quarterback on offense. Belichick lauded Tebow's smarts and work ethic shortly after the team signed him in June, indicating that he'd play whatever role was most beneficial to the team.
Mallett, who finished 9-for-18 for 97 yards, said after the game that his head was "fine."
Asked his overall thoughts from his performance, Mallett said, "You have to see the film, see what went well, what didn't go so well. We'll see tomorrow. ... There are things we have to work on. We'll look at the film and see what they were and go back to work tomorrow."
Information from ESPNBoston.com's Mike Reiss was used in this report.