Cutler was sacked nine times in the first half and took several hard hits, two which caused fumbles.
"You can only take so many hits," Smith said.
The coach added that Cutler will play in Week 5 against the Carolina Panthers if he is "healthy and ready to go."
Veteran Todd Collins started the second half for the Bears. Collins also left the game with an injury after taking a hard hit in the fourth quarter.
"It's tough to see anyone get hit like that, especially our quarterback," Bears linebacker Brian Urlacher said of Cutler. "I don't know what happened, but he didn't go back in so it's probably not good."
The Associated Press contributed to this report.