Garoppolo's long pass came during the media-access portion of practice, as he was warming up for an individual drill in which there was no pass rush.
Before the practice, Garoppolo was unsure of his availability for Sunday's home game against the Buffalo Bills.
"We'll see. I don't know right now," he said. "We have to get there and we'll assess it then, I guess. ... It's hard to predict what you'll feel like in three, four days."
Garoppolo said he had never previously sustained an AC sprain, which was the result of being driven to the turf by Miami Dolphins linebacker Kiko Alonso in the second quarter of a game Sept. 18. He missed the Patriots' 27-0 win over the Houston Texans on Sept. 22.
Rookie quarterback Jacoby Brissett, who started in his place against Houston and injured his right thumb in the third quarter, said his grip on the football wasn't compromised and his thumb and wrist were taped at Wednesday's practice.
"I played with it, so it was fine. I didn't think about it," Brissett said before practice. "Whatever it is you have, you just go out and deal with it."
Both Garoppolo and Brissett were listed as limited participants during Wednesday's practice.
The Patriots will specify the level of practice participation for Garoppolo and Brissett on their injury report later Wednesday. The club doesn't have another quarterback on the 53-man roster or practice squad, which is an indication that Garoppolo and/or Brissett will be available Sunday.
Garoppolo, speaking publicly for the first time since the injury, said he initially felt as if the wind had been knocked out of him.
"You just have to be smart, I guess. It's kind of one of those plays, it's football and stuff like that is going to happen, but you have to be smart in those situations," he said. "After it's all said and done, it's easy to say [you should throw it away]. It's kind of one of those things, you're in the heat of the game. Just bottom line, I have to be smarter than that."
Garoppolo said he never felt any pressure from the Patriots to play Thursday and that he's improving on a day-by-day basis.
"Yeah, no doubt," he said. "That's all you can really ask for right now."