The Longhorns (5-7, 3-6) finished with their third consecutive losing season under Strong, who is 16-21 in three seasons at the school and 12-15 in Big 12 Conference play.
At his postgame news conference, Strong was asked if his Longhorns tenure is over.
"I've not been told," he said. "I just told our players that I look forward to coming back and make sure we get this thing on track."
Strong made a nearly four-minute-long statement to open his news conference Friday night, urging his players never to quit on themselves and expressing frustration about the pressure they've endured the past two seasons while he has been on the hot seat.
"I just felt like every year it turned into being all about me, and it should never have been all about me," Strong said. "It should have been about those guys being given an opportunity to enjoy the game. It never happened for them. They felt it. That's what's so disappointing, is they felt they had to defend me at every turn."
D'Onta Foreman, the nation's leading rusher, was in tears as he walked off the field at DKR-Texas Memorial Stadium on Friday night. He said Strong has meant a lot to him and that seeing his coach go through this "really hurts me."
"I've invested so much into this program, so much into the team, and to come up short like that and for him to have to go through the stuff he's going through is very emotional," Foreman said. "He's a great guy, and he doesn't deserve it, honestly."
When Strong was asked how he would want fans to remember his legacy at Texas, the coach said he hopes to not be judged solely on wins and losses.
"I know that's the way we are all judged," Strong said, "but it's also about the impact that you make on young people's lives."
Strong said he intends to point out Texas' potential to win big in 2017 when he meets with university president Greg Fenves and athletic director Mike Perrin. It was something Strong stressed during Monday's news conference when he defended the program's progress in his three seasons.
"I was told three years ago, when I came in here, to build a program," Strong said. "Just look at the positives, look at where we are with this football team, how young we are. The wins and losses, they don't add up. But still, it's more than just that. It's all about the total development, taking the program and moving it in the right direction."
If Strong is fired, Texas is expected to pursue Houston coach Tom Herman.
LSU also had zeroed in on Herman, but the Tigers have removed the interim tag from Ed Orgeron and have hired him as their new coach, sources confirmed to ESPN on Saturday.
Texas players, meanwhile, rallied behind Strong on Monday and expressed hope that a win over TCU would secure Strong's job for another year. After the 31-9 loss to the Horned Frogs, the players acknowledged the speculation and scrutiny that Strong and Texas faced this week was difficult to avoid.
"Everybody knows in the back of their head what's going on," said linebacker Malik Jefferson.
ESPN's Chris Low and Brett McMurphy contributed to this report.