The past two Sundays, Jack Del Rio and his Raiders have gotten on their tippy toes and reached for victory, only to have it slide just out of their grasp both times. So here they stand at 2-3 heading into their bye week, looking forward to pushing themselves to the limit again in a couple of weeks.

“I enjoy the thrill of us competing the way we do,” the head coach said Monday. “The ups and downs are part of football in the NFL. You can’t be afraid to go back to that place.

“You go back to that place where you execute and you make the play, and you go home happy. If you don’t, then you don’t.”

Losses build character and a hardened sense of what it takes to win.

“That’s a good place to start,” Del Rio said. “That’s certainly not where we’re going to end — that’s not the end point. Like I said, it’s a good place to start.”

The Raiders will use the bye week to work on their running game. Oakland averaged 2.9 yards a carry in the losses to the Bears and Broncos.

“The run game is a team game,” Del Rio said. “You go up against some fronts that are a little stouter than others. I think, talking about yesterday’s game, I think they did a pretty solid job of stopping the run.”

Running back Latavius Murray was benched on the final drive in Chicago on Oct. 4 — after a fumble and an interception where the ball bounced off his chest — and was on the sideline again for most of the second half Sunday against Denver.

Murray has a banged-up shoulder but was ready to go back in, Del Rio said.

“All I would say on that is he is one of many guys that are giving it up for the team, playing hard, playing through some pain in some situations,” Del Rio said. “I’m really appreciative of that, respectful of that, and we’ll continue to do the best we can to put the best product out there.”

Del Rio also touched on the game-deciding interception and the 4th-and-19 screen-pass call that went for 4 yards.

On the fourth-quarter interception that Denver’s Chris Harris returned for a touchdown, Del Rio said quarterback Derek Carr and receiver Seth Roberts share some blame.

“It was a hot situation,” Del Rio said. “The receiver could have gotten his head around an instant quicker. The quarterback could have been slightly more in front with the ball. It could have turned into a great catch-and-run opportunity.”

Later, Oakland was facing a 4th-and-19 and Carr threw a 4-yard screen pass to fullback Marcel Reece. The boos were louder than the Blue Angels that flew overhead earlier.

Del Rio was asked if he was surprised by the call from offensive coordinator Bill Musgrave.

“I’d love to have the chance to do do-overs,” Del Rio said. “Monday-morning quarterback has got perfect vision. … Maybe I can do a better job going forward, but you learn from these experiences. We’re growing as a staff.”

Carr motioned to the sideline after the play, putting up four fingers. Did he think he had just thrown a screen pass on 3rd-and-19?

“I didn’t speak with him to ask him that question,” Del Rio said. “I don’t have that answer for you. I don’t think so.”

Briefly: Defensive end Justin Tuck had an MRI exam on his injured shoulder Monday afternoon. ... Safety TJ Carrie held up well despite playing with a chest injury that had him listed as out for the game Friday afternoon. “I’ve never done it,” Del Rio said of upgrading a player in such fashion. “It’s a first for me.”

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