"Kliff has led this program the right way," Hocutt told reporters. "We're not where we want to be, but we're not far off."
Kingsbury entered his fifth season on the hot seat after his team missed out on a bowl in two of the three previous years.
With only five wins going into the Texas game, the Red Raiders (now 6-6, 3-6 Big 12) appeared to be on their way to missing out on a bowl again, and the Longhorns had the lead and the ball late in the fourth quarter. But Texas Tech's Justus Parker intercepted Sam Ehlinger and returned the pick 55 yards, setting up Nic Shimonek's game-winning touchdown pass to Cameron Batson.
After starting at quarterback the entire season, Shimonek came off the bench in place of McLane Carter to lift the Red Raiders to the come-from-behind win.
"Everybody in the entire locker room loves the man," Shimonek said of Kingsbury. "He's an unbelievable coach. We'd all go to war for him."
Before Hocutt's announcement, Kingsbury said Lubbock is where he wanted to remain.
"I love Texas Tech," said Kingsbury, who played quarterback for the Red Raiders in the early 2000s, as well. "Always have. Always will."