"After seeing the replay of the game I saw things that I was unable to see live from the sideline," Stockstill said in a statement Tuesday.
Blunt, a senior, was ejected in the fourth quarter after his second unsportsmanlike conduct penalty of Monday's game against Navy in Fort Worth, Texas.
Replays on ESPN appeared to show Blunt trying to gouge the eye of Navy quarterback Keenan Reynolds, the (Nashville) Tennessean reported Wednesday.
Navy won the game, 24-6.
Stockstill's apology included an assurance he "will take steps to ensure out team understands the importance of proper behavior."
Blunt issued an apology as well, the newspaper said.