Texans coach Gary Kubiak said that he still "believes" in Schaub, who has helped lead Houston to back-to-back AFC South division titles and the only postseason appearances in franchise history.
"I believe in Matt," Kubiak said at his season-ending press conference Monday. "He's the quarterback of our football team. I've got no doubt about him."
The Texans have gone 19-7 over the past two seasons in games started by Schaub, who missed last year's playoffs due to a foot injury.
Schaub passed for 4,008 yards this season but struggled down the stretch, throwing three touchdowns and five interceptions over Houston's final six games -- including two postseason contests. The Texans went 2-4 in those games.
"I think over the course of the last two years, he's won 70-plus percent of his starts," Kubiak said. "That's hard to do in this league. I feel very good about our quarterback. Our whole team has got to get better -- that includes coaching and playing -- for us to take the next step. And Matt is part of the team, but I've got a lot of confidence in him."
The Texans have been widely criticized despite going 12-4 this season, the best regular-season record in franchise history, and reaching the AFC divisional playoff round for the second straight year. Houston's season ended in disappointing fashion Sunday with a 41-28 loss to the New England Patriots.
Much of the criticism from fans and media following the loss has been directed at Schaub, who threw an interception in the third quarter Sunday to end a drive that could have cut New England's lead to less than a touchdown. He also threw for 343 yards and two scores in the loss.
But Texans star defensive lineman J.J. Watt backed Schaub, echoing Kubiak's sentiment that the team believes in the 31-year-old quarterback.
"If you want to sit here and question our quarterback, that's fine," Watt said. "But every guy in this room believes in him, and we all trust in him and we all believe that he can take us there. We're not going to listen to what the outside world says."
Although Schaub orchestrated a Texans offense that gained 425 yards from scrimmage Sunday, he made a costly mistake in the third quarter when he was intercepted by New England's Rob Ninkovich at the Patriots' 31-yard-line, thwarting a promising drive when Houston faced a 24-13 deficit.
New England quickly capitalized on Schaub's interception, scoring a touchdown to take a 31-13 lead less than three minutes later.
"It's not on (Schaub) at all," Texans left tackle Duane Brown said. "We had plenty of opportunities to make plays. He put the ball in some great spots. Plays weren't made, and we didn't get the running game going as well as we could have up front. So it's not on him. Being a quarterback, people tend to point fingers at him first, but he's been a great leader and a great player for us all year. Definitely not his fault that we lost the game."
"Matt is our guy," center Chris Myers added. "He's our team captain. He's always going to be, and whatever happens, happens. As players, as a team, he's our leader."
Kubiak believes putting all the blame for the loss on his quarterback is unfair, and said that a number of players, including Schaub, didn't make plays that could have changed the outcome. He has no plans to make any changes at the position in the future.
"I would talk about Matt like I would talk about every player on our team," Kubiak said. "We left a lot of plays on the football field as a football team, and when you're playing a great team like that, you can't leave any. There's plays for him to make, but he did make a lot of plays, too.
"We could help him. We could have got him off to a great start if we make the play early in the game. Those plays help a quarterback. It goes with the territory. He understands that, and he's tough enough to work through that."
Information from The Associated Press was used in this report.