The Dundee skipper returned to the first team on Boxing Day having been out of action since August due to a groin problem.
But he was stretchered off at McDiarmid Park with what appeared to be a serious knee injury, and Smith is fearing the worst.
"Potentially it's a serious injury but I can't say what it is until he's been checked out. But it didn't look too good," said Smith. "I'm gutted for him because he's had a really hard time for the past four months.
"To come back, in his third game, and potentially have something bad happen to him is very difficult."
Dundee are now nine points adrift of Ross County at the bottom of the SPL, and Smith was targeted by a section of fans demaning his removal.
But he added: "The fans are entitled to their opinion. I know what I'm doing and I know that the club will get out of the position with me there.
"I got stick as a player at Dundee and I came through it stronger. I'll get stick as a manager and I'll come through it stronger again.
"I've got a lot of affinity with the club. I want to make sure they stay in this league. I'll continue working as hard as ever, if not harder, to make sure we do so."
It is understood that the Dens Park board will meet later this week to discuss the manager's future.