— Often heralded as an offensive genius, Redskins Coach Mike Shanahan entered Sunday’s game between Washington and the Buffalo Bills having never suffered a shutout in 267 games as a head coach.

That all changed on Sunday when Shanahan’s Redskins traveled north of the border and were blanked, 23-0, in front of a Rogers Centre crowd of 51,579.

Still reeling from the injuries that have decimated their offense over the last two weeks, the Redskins found themselves overwhelmed and embarrassed in an outing that also saw them give up nine sacks, equaling a franchise worst.

“That’s as bad as I’ve been involved with from an offensive side as an assistant or a head coach,” a bewildered-looking Shanahan said after the loss. “. . . To score no points, I don’t think I’ve ever had that since I’ve been a coach — assistant or head coach, college or professionally. So it’s pretty humbling to take that.”

The shutout was the Redskins’ first since Dec. 27, 2009, when a squad led by Coach Jim Zorn fell, 17-0, to the Dallas Cowboys.

The defeat dropped the Redskins to 3-4 on the season and extended their losing streak to three games, and four of their last five.

“Makes you feel like you really didn’t do anything. . . . Don’t feel like much of nothing went right today,” said wide receiver Jabar Gaffney, who had four catches for 40 yards.

Just three weeks ago, Shanahan and the Redskins were in their bye week with a 3-1 record and in sole possession of first place in the NFC East. But a quarterback change and a slew of injuries later, the wheels are coming off the Redskins’ season.

Judging by the way the Bills’ defensive players surrounded and swallowed up Redskins quarterback John Beck over and over again, it was hard to tell that that unit had entered Sunday’s contest with a measly four sacks on the season — worst in the NFL.

Against Washington’s line, which features replacement players at left tackle, left guard and center, the Bills pillaged the Redskins, holding them to 178 yards on offense. That output marked the fewest yards Washington has generated since it put up 160 during a game in 2007.

Beck found himself throwing to a revamped receiving corps. Top wideout Santana Moss is out with a broken hand and veteran tight end Chris Cooley is on injured reserve. But given how freely the Bills came through the line to harass the quarterback, it didn’t really matter who Beck was throwing to. When Beck did have time to throw, he struggled with accuracy — particularly on deep passes — and finished the game completing 20 of 33 passes for 208 yards and two interceptions.

“I don’t have any answers right now,” Beck said. “I want to see the tape. It’ll be very telling and I want to use that tape to make sure it doesn’t happen again. . . . I’m sure some of [the sacks] were on me there. As the quarterback, it’s part of my job to get the ball out of my hands, so I want to check that out on tape and see how I can help my guys out.”

It also mattered little that the Bills entered the game ranked 30th against the run. Running back Ryan Torain — who took over for Tim Hightower, who also is on injured reserve — found daylight hard to come by and mustered only 14 yards on eight carries.

With yards and big plays so difficult to attain, the Redskins needed a strong outing from their defense as they faced a Bills offense that ranked third in the NFL, scoring 31.3 points per game. Washington’s defense had an uneven performance, however, giving up chunks of yardage through the air and on the ground. It allowed Bills quarterback Ryan Fitzpatrick to pass for 262 yards, including two scoring passes to tight end Scott Chandler, and Buffalo running back Fred Jackson to gash them for 120 yards on 26 carries as the Bills improved to 5-2.

Washington’s defense presented the offense with a golden opportunity early in the second quarter. Linebacker Brian Orakpo recovered a fumble on a botched Buffalo snap, giving Washington the ball at the Buffalo 31-yard line, the closest the Redskins had been to the opposing end zone at that point.

But Beck was sacked twice in six plays, and Washington had to settle for a 49-yard field goal attempt. It was blocked at the line by Spencer Johnson.

The Bills, who took over at the 39, then went 42 yards (34 of them on a pass interference call on Josh Wilson) before scoring a field goal to go up, 10-0.

As the quarter reached its final minutes, the defense came up with another clutch play, but the offense squandered another opportunity. The Bills marched downfield and reached the Washington 8-yard line when linebacker London Fletcher — playing in his league-leading 215th consecutive game despite a hamstring strain that hampered him all week — picked off a Fitzpatrick pass in the end zone.

But Beck was sacked a fourth time, and Roy Helu was stopped short of the first-down marker on a third-down pass play, and Washington again was forced to punt.

Buffalo, ahead 13-0, opened the third quarter by going 80 yards on seven plays to score on another Fitzpatrick-to-Chandler connection — this time from 15 yards out. Buffalo added a field goal in the fourth quarter to account for the final score.

“We got beat down,” cornerback DeAngelo Hall said. “I stopped really looking at the scoreboard. I didn’t even know it was 23-0. It’s frustrating. It’s frustrating to not be able to get some things going. Defensively, I felt like we knew what was coming and we still couldn’t stop them.”