The Titans' playoff hopes are all but over following back-to-back losses to the Indianapolis Colts and the Denver Broncos leading to speculation over the future of Munchak.
Smith replaced his father-in-law Bud Adams as owner of the team following his death earlier this season.
"Bud in the past would fire people at the drop of a hat," Smith told the the Tennessean. "I think sometimes you need to keep the gun in the holster. I think we need to sit here and look at these three weeks, and let's play hard.
"Let's see if we can win some games. When we sit down with Mike at the end of the season I expect Mike to come in and tell me why he thinks we're in the position we are, what he thinks needs to be done for us to improve."
Munchak has been head coach of the Titans since the 2011 season when he replaced Jeff Fisher.