Carlos Hyde doesn’t have a fumbler rep, but the 49ers’ rookie backup running back coughed up the ball on the first play of the second quarter Sunday, giving the rock to Washington near midfield.

“I just felt like I let everybody down,” Hyde said. “It took me a minute to get over that play.”

Frank Gore, durable as he is, can’t carry the entire rushing load for the 49ers. They need Hyde, but they didn’t go back to him until the fourth quarter. Running backs coach Tom Rathman told Hyde, “You’re up. Two hands on the ball.”

Hyde said, “I was ready.”

On 1st-and-10 with 4½ minutes to go, Hyde picked up 5 yards, to the Washington 14, on what looked like a zero-gain play. Two plays later, he slashed through a nice hole in the defense for a 4-yard touchdown that gave the 49ers the win.

“I saw a big hole, you coulda run through there,” Hyde said to a sportswriter, and that’s a high compliment to Hyde’s blockers. “I was one-on-one with the safety. With a full head of steam going into the end zone, I doubt if anyone could stop me on that play.”

Hyde’s blockers believe he runs better than the average sportswriter.

Fullback Bruce Miller credited the offensive line for the hole on that play, but added, “When he gets going downhill, he’s pretty tough to bring down. I know he took a hit but he shook it off and got into the end zone. Just a good job by the guys up front and a good job by Carlos getting his pads downhill.”

Tackle Joe Staley called Hyde “a one-cut runner,” someone who doesn’t get cute or dance much.

Scott Strazzante / The Chronicle

“Yeah, I don’t try to do any” dancing, said Hyde, who’s 6-foot, 235 pounds. “That’s what I call a scatback, the guy who dances around. I’m not a scatback. I just try to get my pads north and south and get to the end zone.”

Hyde didn’t have a big stat day (seven rushes for 16 yards), but head coach Jim Harbaugh said, “I thought he was running it inspired. Had the fumble, (but) he was locked into the mission. You can tell by the way he was running the football.”

Hyde said he hoped the two big runs on that game-deciding drive showed his teammates and coaches that he can be trusted.

“We’ll see,” he said. “I fumbled and they put the ball back in my hands. That told me a lot. So just keep trying to build that trust with my coaches so they can put the ball in my hands more.”

Scott Ostler is a San Francisco Chronicle columnist.