“Everybody said, ‘Well, you only had nine points,’ “ Redskins Coach Mike Shanahan, left, said of the Rex Grossman-led offense against Miami. “But nine points obviously goes to a collective group. But I thought Rex played well.” (Hans Deryk/Associated Press)

As Washington Redskins players warned that victories could become increasingly difficult to come by, Coach Mike Shanahan said Monday that he’s sticking with Rex Grossman at quarterback for one simple reason: the turnover-prone veteran gives the Redskins the best chance of another victory.

The Redskins haven’t won a game since Grossman was benched in favor of John Beck Oct. 16. Washington carries a five-game losing streak into this weekend’s game against the Dallas Cowboys. Shanahan said he hopes a second midseason quarterback switch might change the team’s fortunes.

The Redskins’ offense failed to score a touchdown with Grossman under center in Sunday’s 20-9 loss at Miami, but Shanahan said Monday he didn’t need to wait before anointing Grossman this week’s starter.

“I was impressed with the way he played, with the way he handled himself,” Shanahan said. “Everybody said, ‘Well, you only had nine points,’ but nine points obviously goes to a collective group. But I thought Rex played well.”

As the team’s chances of competing in the NFC East have faded with each passing week, some players say the season is teetering in the balance. The offense can’t score, and “there’s no guarantee that we can win another game,” said nose tackle Barry Cofield.

“If we don’t play better,” he added, “there’s no reason to expect to win any games. The ball’s not going to just bounce our way. It could get very ugly. It could get historically ugly.”

Already, the Redskins are mired in their worst losing streak since 2001 — and the longest of Shanahan’s coaching career. Even with Grossman back in the lineup, the task this weekend against the rival Cowboys will be difficult. Dallas is coming off a 44-7 win over Buffalo, a team that shut out Washington two weeks ago.

While wins have been elusive, injuries continue to pile up for the Redskins. Monday, Shanahan said the team has lost rookie wide receiver Leonard Hankerson for the season with a torn labrum in his hip. He becomes the fourth offensive starter to hit the injured reserve list, joining tight end Chris Cooley (knee), running back Tim Hightower (knee) and guard Kory Lichtensteiger (knee). Three other players who have started games this season — wide receivers Santana Moss (finger) and Niles Paul (toe) and right tackle Jammal Brown (groin) — likely will miss Sunday’s game against Dallas because of injuries.

“Like I’ve said from Day One, it’s just not one guy that runs an offense. It’s 11 guys working together,” Shanahan said. “What I’m trying to do is get the best chemistry and do the best thing for our offensive football team.”

Grossman led the Redskins to a 3-1 start but was benched after throwing four interceptions against Philadelphia. Beck largely struggled in his three starts, and after splitting first-team reps with Grossman last week , Grossman regained his spot in the lineup prior to Sunday’s game at Miami. The demotion last month apparently didn’t deter him.

“I thought Rex did a good job of concentrating and doing his job on the scout team or the few reps he did get with the first unit,” Shanahan said. “I don’t think Rex really does get down. He’s a guy that’s up most of the time.”

Grossman completed 21 of 32 passes for 215 yards on Sunday but threw two interceptions and failed to produce a touchdown. Despite having played only six games this season, Grossman has thrown more interceptions (11) than all but three other NFL quarterbacks. He has thrown an interception on 5.6 percent of his pass attempts this season, by far the highest percentage in the NFL. The next closest is Kyle Orton’s 4.5 percent. Since 1999, only Tampa Bay’s Josh Freeman has posted a higher single-season percentage (6.2 percent in 2009).

While Shanahan had pronounced Beck the team’s starter early last week, he said Monday he doesn’t anticipate a similar flip-flop before this weekend’s kickoff. “Unless there’s an injury during the week, Rex will be the quarterback,” he said.

While injuries continue to force coaches to shuffle the lineup, they hope returning Grossman to the huddle might stabilize a besieged offense.

Only two NFL teams — Jacksonville and St. Louis — - have scored fewer than Washington’s 11 offensive touchdowns this season. The Redskins had to settle for three field goals against the Dolphins, and haven’t found the end zone in the first half of a game since Oct. 2 at St. Louis. That game not only marks the Redskins’ last win, it also stands as the last time they even held a lead.

The constant roster shuffling since then hasn’t aided the team’s production, players say.

“It’s very frustrating, especially when you couple it with losing,” said wide receiver Anthony Armstrong, a starter last season who has just one reception during the five-game losing streak. “You get a win and a lot of that stuff kind of gets brushed under the rug. I think a win will cure a lot of this indecision and controversy stuff going on.”

Beck’s future with the team is a bit in doubt. It’s not clear whether he’ll get another opportunity to show coaches that he’s capable of starting at quarterback. He’s still winless in seven career starts. Though some of the teammates around him were battling injuries, Beck’s three-game stint as the Washington starter was unimpressive.

“As I said, I like John’s talent, I like what we have in John,” Shanahan said. “But I’m always going to do what I think is in the best interest of the team to win.”

Staff writer Eric Detweiler contributed to this report.