Smith, who is currently in competition with Mark Sanchez for the starting quarterback jersey, suffered a mild sprain to his ankle during Friday's pre-season match against Detroit but still took part in practice yesterday.
The rookie was in noticeable pain at times during the session, but revealed that offensive coordinator Marty Mornhinweg's stories of legendary quarterback Brett Favre inspired him to play through the pain.
"Marty told me about Brett Favre and how he played through pretty much every single injury," said Smith. "I try to be the same way.
"You can't miss a day of practice. I pride myself on being out there at all times, and one little ankle injury wasn't going to stop me from practicing with my teammates."
Smith was selected by the Jets as the 39th overall pick in this year's draft.