The Warriors moved back to the top of the table meaning a bonus-point win away to Ulster in Belfast next Friday would secure home advantage throughout the play-offs.
Glasgow did suffer a few injury scares during the 40-17 win over Cardiff, with Rory Darge, Alex Samuel and Sione Tuipulotu all forced off. However, Tuipulotu's issue was only cramp, while Smith sounded confident about both Darge and Samuel.
"It's a rib cartilage injury," said Smith. "A little bit of a contusion injury so it will all depend on how quickly they recover. But it's not that serious, it won't keep them out for the rest of the season if I can put it that way."
Speaking about Samuel, Smith added: "Yeah, he twisted his ankle again. I think somebody wrote today that we've used our 10th or 11th lock pair for the season. Every year it's been like that, that our second row gets under scrutiny from a lot of injuries. He's all right, I think."
Huw Jones was also seen wearing a moon boot while collecting his leaver's jersey after the match, but Smith remains hopeful the British & Irish Lion can still feature once more for Glasgow.
"Yeah, he injured his toe against the Stormers," revealed Smith. "Underneath his toe. But he'll be weaned out of the boot now over the weekend so he should be back, not training at all but back running or moving at least without the boot from next week on."
Although reluctant to make any firm guarantees, Smith also struck an optimistic tone regarding the possible returns of Jamie Dobie, Scott Cummings and Gregor Brown in the near future.
He said: "The aim is to have them all available for the quarter-finals so there's a couple of weeks to get them ready. I hope so. I don't want to create any expectations. The medical team is managing my expectations as well so we will see.
"There's three weeks now for us to make sure and like I said I believe injuries happen for a reason. These guys coming back from injury now will be fresh and reset in different other ways. So hopefully it will make selection hard when they're all back."