Patriots quarterback Tom Brady would never turn his back on a win, but in the wake of Sunday’s victory against the Jets, he seemed a little peeved at the play of the New England offense.

Over the course of the first four weeks, the Patriots offense was a well-oiled machine -- setting aside the terrific statistical performances from Brady and Wes Welker, entering Sunday’s game against the Jets, New England had just five three-and-outs over the first four games of the season. The Patriots were averaging 7.5 yards per play, best in the league, and were at or near the top of the league in every major offensive category.

But on Sunday against the Jets, New England stalled a few times in the red zone (and turned the ball over on the doorstep of the New York end zone), took a season-high six negative plays (Brady was sacked four times, matching his total from the previous four games) and was whistled for some inopportune penalties.

As a result, for Brady, the win had a bittersweet taste.

“I don’t know -- I expect a lot out of our team just like our coaches do and all the players do, but I thought we were capable of playing better than we did [Sunday],” Brady told WEEI on Monday.

“Believe me, I know how tough it is to win and how much it sucks to lose,” he added. “We played a good team [Sunday] that has been a tough opponent for us and is a tough opponent every single time we play them, but I thought that we made it a little tougher than we needed it to be.”

Keeping in mind that it’s all relative -- most NFL offenses would kill for problems this minor -- here are three examples of what Brady is talking about.

• Struggles in the red zone. New England was 3-for-6 in the red zone, with the most painful miss coming at the end of the first half when the Pats turned the ball over at the goal line after a Brady pass for Aaron Hernandez was bobbled and ended up getting scooped up by Antonio Cromartie.

• A season-high six negative plays. Four sacks and two negative runs combined with six penalties created some less-than-optimal situations for the New England offense.

• An inability to truly finish off the Jets. A frustration of several offensive players, not just Brady. New England had a balanced offense, particularly in the second half, but the Patriots were unable to muster a fourth-quarter touchdown against New York, settling for a pair of field goals, the last of which made it a two-score game and finally put the game out of reach with just over a minute to go.

With the Cowboys coming to town on Sunday -- a fast, aggressive defense that is one of the best in the league in almost every category -- what do the Patriots need to do to fine tune their offense? Here are a few likely points of emphasis for the New England offense this week.

• Some of New England’s struggles in the red zone against the Jets could be attributed to the fact that the two of their most dependable red zone threats were not at full strength. Aaron Hernandez was gutting his way through a knee injury, while Rob Gronkowski -- one of the most dependable red-zone threats in the league since the start of last season -- was fighting an illness. (Gronkowski had nine red zone touchdowns last year, which led the league.)

• There’s also the need to steer clear of negative situations, as well as maintaining offensive rhythm. Sunday aside, the Patriots have been pretty good this year about staying out of negative plays -- they entered the game with only eight negative plays from scrimmage all season, and have cut back considerably on harmful penalties over the last two weeks. Mistake-free football against an aggressive defensive front like Dallas is key.

• When it comes to pass protection, look for more help along the offensive line in the form of tight end Dan Gronkowski, who was reportedly re-signed by the Patriots on Monday night. There’s also the possibility of the return of right tackle Sebastian Vollmer, who has been hobbled this season with a back problem.

• In addition, staying out of three-and-outs has been paramount to the success of the Patriots offense this season -- they have just six three-and-outs in 56 possessions this season, excluding end-of-game scenarios, and have used that offensive sustainability to string together some lengthy drives.

One thing to look for this week against the Cowboys is how the Patriots use the no-huddle. It’s something the Patriots offense has been able to utilize when the Pats know they have a defense reeling -- entering Sunday’s game, New England had been in no-huddle for 21 percent of its snaps over the first four games, running it during key stretches in hopes of generating momentum back to its favor. Against the Jets, the Patriots used it on 15 of their 72 plays (also 21 percent), and used it effectively on two drives: one at the end of the second where they got down to the Jets’ 11 before the Cromartie pick, and the other on an 11-play scoring drive at the end of the third that culminated in a 3-yard touchdown run from Green-Ellis.

The no-huddle allowed the Patriots to keep the Jets on their heels -- New England gained an average of 5.5 yards per play in the no-huddle against New York. The Jets couldn’t make the personnel adjustments it needed, and New England was able to pick up key yardage as a result. This was never clearer than late in the third quarter when Brady called a play when the Jets weren’t set, and the quarterback found Green-Ellis split right with no New York receiver within 15 yards of him. The running back hauled in the pass and rumbled 13 yards down to the Jets’ 3-yard line. (On the following play, the discombobulated New York defense had just 10 players on the field before New England called a timeout.)

“We saw that in the San Diego came, a couple of times with [Deion] Branch,” Patriots coach Bill Belichick said. “You get a guy out there and somebody doesn’t adjust out. The quarterback should always do that when he comes out, looks over, sees the whole field and sees a guy uncovered. Or maybe a bad matchup, maybe there’s a linebacker on a receiver or something. They just end up that way. Tom was able to take advantage of it.”

The Patriots will get another crack at a similar unit this week when they face Dallas, as it’ll be the second straight week they’ll face a team where one of the Ryan brothers runs the defense -- last week, it was Rex and the Jets. This week, it’ll be Rob Ryan, who serves as the defensive coordinator for the Cowboys.

“There’s definitely some carryover. I wouldn’t say they’re exactly the same but there’s definitely some carryover,” Belichick said when asked if there are similarities between brothers’ two defensive schemes. “Both [are] based out of the 3-4 but use a lot of different looks. Both defensives use a lot of multiple defensive backs: four, five, six, seven. There’s a lot of carryover in some of those respects.”