Tolzien threw two interceptions that were returned for touchdowns and had only 128 yards before being replaced. The Colts had 225 yards of total offense and were 0-for-10 on third down against the Rams.
On Friday, when asked about the team's quarterback situation, coach Chuck Pagano said: "We're not ready to announce it yet. ... Whoever we trot out there is going to play well. They're ready."
Brissett, who has better mobility and arm strength, has been with the Colts since Sept. 2 after being traded from the New England Patriots.
"You have to make some adjustments," offensive coordinator Rob Chudzinski said this week of Brissett. "He's been here a week, so getting to know him is as important as him getting to know the playbook. That's a process that happens over time. ...
"I've been impressed in the short amount of time that he's been here. It would be a very challenging situation. But he's the type of guy -- smart, very poised, and I like some of the things I've seen on the field just from his physical tools, as well."
Brissett's former teammates in New England were happy to see him get another chance as an NFL starter.
"I'm happy for him, I really am," Patriots QB Jimmy Garoppolo said Friday. "He's a great guy, a great friend of mine. I wish him nothing but the best. It's exciting."
Regular starter Andrew Luck, who signed a six-year deal worth $140 million in June 2016, has yet to play for the Colts this season after having right shoulder surgery in January.
ESPN's Mike Wells contributed to this report.