Burcham was under pressure throughout the day and was never able to get going as the Mustangs suffered their first shutout in nine years.
John O'Korn finished 25 of 41 for 245 yards and two touchdowns to lead Houston over SMU 34-0 Friday, snapping the Cougars' three-game losing streak.
Burcham finished 27 of 52 for 212 yards and threw 3 interceptions for SMU (5-6, 4-3 American).
"He did enough good things that we could have won the game," SMU head coach June Jones said of Burcham. "The mistakes compounded things for him. I tried to take the pressure off him by calling more running plays, but we just couldn't get anything going.
Jeremy Johnson had 8 receptions for 75 yards, and Darius Joseph caught 9 passes for 52 yards, while Prescott Line rushed 17 times for 81 yards for SMU, which finished 3 of 7 on fourth downs and gained 295 yards.
The Mustangs, who entered the game averaging almost 31 points, were held to scoreless for the first time since 2004 when they were shut out 42-0 at Fresno State.
Jones called the loss very disappointing.
"Whenever you play a young quarterback, everybody has to pick up their game," Jones said. "I thought our defense played good other than that first possession, but offensively we didn't do what we needed to do."
Daniel Spencer caught seven passes for 100 yards and a touchdown, while Greg Ward, Jr., had five receptions for 48 yards and a touchdown. Ryan Jackson rushed seven times for 62 yards and a touchdown, and Kent Brooks added a touchdown run for the Cougars, who totaled 365 yards.
Houston forced four turnovers — three interceptions and a fumble — and also had five sacks. Zach McMillan had two interceptions.
Burcham said he pretty calm and was anxious to get going at the start.
"I am very critical of myself," Burcham said. "I have a lot to improve on. I made some throws that I was not supposed to. I have to be smarter and make smarter throws."
Houston (8-4, 5-3) earned its first shutout since 2011 and its first conference shutout since a 64-0 win over Rice in 1989.
O'Korn found Spencer on Houston's first offensive play for a 67-yard touchdown pass with 13:32 left in the first quarter to open up a 7-0 lead.
After Burcham was intercepted by Adrian McDonald to give the Cougars possession at SMU's 29, Kyle Bullard upped the lead to 10-0 with a 27-yard field goal with 5:23 left in the first. Bullard added a 27-yard field goal with 2:48 left in the third.
"We did not have enough plays to make it happen," Burcham said. "I blame myself for a lot of it."
O'Korn found Ward for a 19-yard touchdown grab two minutes into the second quarter to up the lead to 17-0.
Brooks extended Houston's lead to 24-0 with a 1-yard touchdown run 34 seconds before halftime after Eric Eiland set the Cougars up with a 62-yard fumble return off a bad snap down to the SMU 1 before being tackled by SMU's Kevin Pope.
Jackson added a 33-yard touchdown run with 8:07 left in the third to give the Cougars a 31-0 lead.
SMU struggled moving the ball in the first half, gaining 53 yards and two first downs in the first quarter and 146 yards in the first half to go along with three turnovers and 9 penalties for 75 yards.
Both times SMU got inside the Cougars' 35 in the first half resulted in turnovers - the first a McMillan interception in the end zone when SMU reached the Houston 22 and the second was Eiland's fumble recovery when the Mustangs were at the Houston 32.
SMU got in the red zone with five minutes left in the fourth, but Line was stopped a yard short of the first down on fourth and 6 from the Houston 15.
"With a young quarterback, we have to catch the ball and make plays to take some pressure off," Jones said. "I thought he did some good things, but if we make those plays early, then he gets confidence and everybody gets excited. I think that could have changed things. But we didn't make those plays."