Kubiak collapsed while walking off the field at half time and was taken to hospital, where it was confirmed that he had not suffered a heart attack.
Smith revealed that the incident was not as serious as first feared and hopes to have the 52-year-old back within a day.
"He had an episode, he was light-headed and dizzy. He was evaluated by a number of specialists, he is awake and coherent," Smith told NBC after the match.
"We have to assess. Obviously, there's a lot of info. Hopefully, Gary will be back with us tomorrow."
The Texans led 21-3 at half time but were seemingly rattled by the loss of their coach and went on to suffer a 27-24 defeat.