LaFleur, asked if Brissett would be on the Cardinals past the trade deadline, said he was only focused on this week. The trade deadline is Nov. 10.
And the call to let Brissett know of the change was "not easy," LaFleur said.
"That's not a fun phone call. There's no book for that. There is a human element to it. I have a lot of respect for Jacoby the person. I have a lot of respect for Jacoby the player. This was not all on him. But the position that those guys sign up for, that's the deal. We needed a spark and obviously Gardner gave us one."
LaFleur said making Beck the backup was "the right thing to do" to continue the rookie's development.
"I know he's prepared to go in there if need be," LaFleur said, adding "he has a full grasp of this game plan, of this system. It's no secret that if something were to happen, it'd be nice to know what we've got (in Beck)."
The Cardinals next play in Seattle, followed by a home game against the Rams and then a trip to Kansas City against the Chiefs.
In the previous seven years of Minshew's career, he has had extended time as a starter as a Jaguars rookie in 2019 (12 starts), in 2020 (eight starts), in 2023 with the Colts (13 starts) and in 2024 with the Raiders (nine starts).
"If you guys have ever seen 'Napoleon Dynamite,' I've always known (Gardner) could throw a pigskin a quarter mile," defensive lineman L.J. Collier said postgame. "Minshew Magic is real."