In addition to an interception and fumble by the senior quarterback and another fumble, the Bobcats couldn't punch it in on four downs from the 1-yard line.
"On the 1-yard (line) twice, can't turn the ball over," he said. "That's all on me. Got two turnovers tonight. I've got to get better at that aspect of the game, but the defense played great tonight. You can drop this one to the offense."
The giveaways set the tone, he said.
"Our defense was playing really good," Arndt said. "I felt like we could have gained a little momentum if we could have punched it in down there. We kind of let them down."
Coach Dennis Franchione agreed.
"Three turnovers on offense, you know we can't do that," he said. "We can't beat teams like this. That hurt."
Backup quarterback Davis Webb threw for two touchdowns and 310 yards to lead Texas Tech.
Webb threw a 4-yard touchdown pass to Eric Ward in the third quarter and a 10-yarder to Bradley Marquez in the fourth after Texas State failed on a fake punt deep in its own territory.
Webb finished 19 for 43 and had two interceptions.
Texas Tech's defense got the lone touchdown of the first half when linebacker Will Smith returned a fumble 9 yards.
Ryan Bustin added four field goals for the Red Raiders (4-0)
Texas State (2-1) struggled against a stingy Red Raiders defense that gave up only 232 total yards. Bobcats running back Robert Lowe scored on a 49-yard run - a career-long rush for the sophomore.
Arndt was 12 for 23 for 108 yards.
Texas Tech finished with 552 total yards.
Jace Amaro caught nine passes for 86 yards and Marquez caught six passes for 84 yards to lead the Red Raiders.
Starting quarterback Baker Mayfield, who was replaced by Webb early in the second quarter, returned to the game late in the fourth quarter. He was 14 for 20 for 124 yards and one interception.
On the Bobcats' opening possession of the second half Lowe's run pulled Texas State within 13-7. Lowe went up the middle before cutting to the far sideline, and he evaded a couple of tacklers once he got inside the 10-yard line.
An ensuing onside kick initially was ruled recovered by the Bobcats but they touched the ball before it had gone 10 yards, so the Red Raiders took over on Texas State's 44. Webb found Marquez for a 39-yard reception before the Red Raiders backup QB found Ward for a 4-yard TD to put Texas Tech up 20-7.
Texas State had just one turnover coming into the game. By halftime the Bobcats had lost two fumbles and Arndt was intercepted by Pete Robertson at the Red Raiders 1-yard line in the first quarter. On its ensuing possession Mayfield moved the Red Raiders to the Texas State 46 and then was intercepted by Xavier Daniels.
Four plays later Arndt fumbled and it was recovered by Terrance Bullitt at the Red Raiders 33.
Texas Tech held the Bobcats from getting into the end zone when Texas State had first-and-goal from the Red Raiders 1.
On the first play of Webb's second series, Justin Iwuji intercepted him at the Texas Tech 35 and returned it to the 11.
After getting a first down at the Red Raiders 1, Texas Tech held the Bobcats from getting into the end zone for four plays, preventing them from cutting into the Red Raiders' 10-0 lead. Arndt couldn't complete a pass to Brandon Smith on fourth-and-goal and the Red Raiders took over on downs.
Texas State running back Terrance Franks fumbled at the Bobcats' 9-yard line and Smith scooped it up and went in for the score to put the Red Raiders up 10-0 early in the second quarter. The Bobcats had taken over after Mayfield ran the ball and lost a yard on fourth-and-1.