According to league sources, the team likely pulled Cutler, who didn't want to come out of the game, for precautionary reasons.
Cutler was sacked nine times in a 17-3 loss to the New York Giants. Smith said Cutler showed symptoms of a concussion after the final sack late in the first half, when Cutler's head banged the turf while he was taken down by Aaron Ross. The Bears then went with a run by Chester Taylor, and Todd Collins replaced Cutler to start the third quarter.
Collins actually wound up leaving with a stinger late in the game, forcing Chicago to go with Caleb Hanie. Smith hopes to have all three quarterbacks available for practice on Wednesday.
"Don't know exactly when [Cutler suffered the concussion]," Smith said. "We saw symptoms after the last sack, and we went in at halftime and made the decision.
"He's feeling OK, as he was last night after the game. We'll monitor and continue to evaluate."
Smith wasn't trying to make an official observation on Monday.
"He's here, and it seems like he's in pretty good shape right now," Smith said. "No visual signs or anything I can tell. That's why I try not to be a doctor, and I leave that to other people. But he seems like he's OK today.
"It's not like he's bed-ridden or anything like that. He's up here today with the rest of his teammates, going through meetings and all that."
Smith didn't want to speculate about Cutler's availability for the Bears' game Sunday against the Panthers in Carolina.
"If anything, we go beyond the call of duty when dealing with our football players," Smith said. "We make sure they don't go back on the football field unless we all feel good about it.
"He went through a lot last night. You don't want your quarterback going through that. As far as him coming back, he wanted to continue playing last night. If Jay is healthy and ready to go, like all players, they'll be anxious to get back out on the football field, and we just have to do a better job of protecting him when he gets back out there."
Guidelines adopted by the NFL in December 2009 say players who leave a game or practice because of a concussion should not resume football activities until they are "fully asymptomatic, both at rest and after exertion" and have been cleared by team physicians and an "independent neurological consultant."
Smith didn't place all the blame for the sacks on the Bears' beleaguered offensive line, which has been battling through injuries.
"There were a lot of thing that were unacceptable from that game," he said. "I'll put the offensive line in there.
"But it's not just the offensive line. We gave up a lot of sacks, and that was spread out. Some of it was the offensive line, the tight ends and running backs had something to do with it, and also Jay. It's a combination of all of those."
Left tackle Frank Omiyale said the breakdowns are "all stuff that can be fixed."
Cutler, who has made 57 straight starts since Denver turned to him as a rookie in 2006, had absorbed more than a few big hits by the time Ross got to him late in the first half.
Cutler got up and took a few steps toward the sideline before correcting himself. Soon after, he had what appeared to be a dazed look when the TV cameras showed him sitting on the sideline, and his decision-making was questionable at best.
"We are responsible when he's hit," Kreutz said.
Cutler didn't help himself by hanging on to the ball too long at times, in an apparent effort to make plays that just weren't there, and the result was more hits from a relentless defense.
Smith wanted to emphasize that the Bears are not panicking despite the loss.
"We played four games and we lost one," Smith said. "Let's not panic around here, all right? The reality is we're 3-1 with this group. Our offense has done a lot of good things. Last night, we didn't get it done. We didn't get it done. No more than that."
Information from ESPNChicago.com's Jeff Dickerson and The Associated Press contributed to this report.