The Raiders’ first playoff game in 14 years is Saturday … and they don’t know who their starting quarterback is going to be.

Relax. Neither do their opponents, the Texans.

It’s a strange set of circumstances four days before kickoff, but both teams are going to try to rally around a wild card at the most important position in Saturday’s AFC wild-card game in Houston.

Oakland, already reeling from Derek Carr breaking his leg Christmas Eve, is waiting to see how Matt McGloin’s sore left shoulder heals after a nasty spill that forced him to leave Sunday’s game in Denver. The other option is rookie Connor Cook, who showed flashes in the 24-6 loss to the Broncos but also threw an interception and lost a fumble.

Cook would become the first quarterback to get his first career start in a postseason game.

“Either way, you know you’re dealing with a tough situation,” head coach Jack Del Rio said at Monday’s weekly news conference. “You’re dealing with your backup — maybe your third-stringer.”

As for the Texans, head coach Bill O’Brien said Monday that he doesn’t know who will start at quarterback. Tom Savage started the last two games but sustained a concussion in Sunday’s loss to the Titans, and a short week doesn’t help him. Brock Osweiler, who was benched for Savage, probably will be the starter — and O’Brien said the decision will not be based solely on health.

“ I think there are a lot of different factors,” he told reporters. “Obviously, health is part of it, no question about it ... (but) we moved the ball well — Brock did a nice job when he was in there, so there’s a lot of different factors that go into it.”

Both coaches are looking for help. The Raiders’ defense didn’t do McGloin any favors by allowing a sluggish Denver offense to march down the field on the opening drive.

“That’s the worst thing you can do for an offense that’s playing with a new quarterback,” Del Rio said. “Now they’re feeling more pressure than they need to feel. So, the reality is ... we’ve won all year as a team, we lose as a team.”

It was a costly loss, as the Raiders kissed goodbye the AFC West crown and a first-round bye. Besides McGloin, receivers Michael Crabtree and Amari Cooper and offensive linemen Donald Penn and Kelechi Osemele are all nursing injuries. And that’s just on offense. Rookie safety Karl Joseph is not yet back from a toe injury, and new starter Nate Allen is in the league’s concussion protocol after being woozy from a hit Sunday.

It’s a concern, getting enough healthy bodies together Saturday.

“A little bit,” Del Rio said. “Yeah, we have a few guys that are banged right now. The short week doesn’t make it any better. We’re excited to be in the postseason. We’ll be energized come game time.”

McGloin short-circuited Sunday, he had so much energy.

“I think the magnitude and the opportunity, I think he pressed a little bit,” Del Rio said.

Before McGloin was knocked out of the game in the second quarter, the fourth-year veteran completed 6 of 11 passes for 21 yards. Cook looked more poised in the pocket when he came in the game, and completed 14 for 21 passes for 150 yards and a touchdown.

“I thought he handled himself pretty well,” Del Rio said. “You know, ball security’s so huge … (but) I thought overall that he did a pretty solid job. That’s a tough set of circumstances for him.”

Made tougher by the fact that the Raiders couldn’t run the ball, and then stopped trying after they fell behind 17-0 by the time Cook entered the game. Del Rio shared some frustration with offensive coordinator Bill Musgrave over running back Latavius Murray’s workload.

“Latavius ends up with five carries. How’s that happen?” Del Rio asked reporters. “It wasn’t a great job of executing by the Oakland Raiders. That’s what it is. We own up to it, and we’re going to put it behind us as quick as possible and move forward.”

Meanwhile, the Raiders signed quarterback Garrett Gilbert to their practice squad, Gilbert’s agent, Leigh Steinberg, tweeted. Gilbert, a 6-foot-4, 221-pounder who played at Texas and SMU, is the son of former Cal and Buffalo QB Gale Gilbert. He was on Oakland’s practice squad in 2015.

Vic Tafur is a San Francisco Chronicle staff writer. Email: vtafur@sfchronicle.com Twitter: @VicTafur