A league source told ESPN NFL Insider Adam Schefter that Okung suffered a torn ligament in his toe.
Carroll would not give specifics on the severity of Okung's injury, saying the team is still awaiting more information before coming to a determination on how long they'll be without their Pro Bowl lineman.
"I know there is some stuff that happened there and we're waiting to figure it all out," Carroll said. "I think it's best just to hold there. If I told you something I'd be making it up."
The most Carroll would reveal about Okung's status was the likelihood that he would be unavailable to play against the Jaguars.
"I don't think that's possible," Carroll said. "We'll see what happens. I don't think he can make that."
Okung was injured on the final play of the first quarter on Sunday night, following a 60-minute weather delay. Seattle quarterback Russell Wilson fell forward in a pile for a 2-yard gain on a third-and-2 run.
Okung walked off the field with a limp and was taken by a cart for further tests at the stadium.
He returned to the sideline and went through some footwork drills, but ultimately spent the rest of the night on the sideline as a spectator.
Short of Wilson or safety Earl Thomas, no Seattle player may be more important than Okung. He's struggled with ankle injuries early in his career and missed the end of the 2011 season with a torn pectoral muscle.
But he started the final 14 regular season games last season and both playoff matchups, serving as an important blindside protector for Wilson.
McQuistan was serviceable but struggled trying to slow down San Francisco pass rusher Aldon Smith, who finished with two sacks and three quarterback hits.
Carroll said it was too early to determine how they would proceed should Okung miss more than just this week.
"We're still taking in information to know what it's all about. We don't know all the details yet," he said.
Carroll also said that backup running back Spencer Ware suffered a sprained ankle late in the win, but that was the only other significant injury.
Defensive end Chris Clemons is expected to practice again this week as he continues to recover from offseason knee surgery. Carroll said if Clemons didn't make it back this week he expects he'll be able to make his debut against Houston on Sept. 29.
Information from The Associated Press was used in this report.