FOXBOROUGH, Mass. – It was a surprisingly dominating win over a major rival that had won three straight games. Now the New England Patriots enter the soft part of their schedule.

Only one of their remaining seven opponents has a winning record. And on Monday night the Kansas City Chiefs are expected to start a quarterback against them who has thrown just 13 NFL passes.

But just as the Patriots’ 37-16 beating of the New York Jets on Sunday night was unexpectedly one-sided, so might a big underdog stun the Patriots, especially if they dwell on their latest success.

“No matter what happened last week, whether we won, lost, at home or on the road or in London, it doesn’t matter. Once that game is over we have to put it behind us,” New England Coach Bill Belichick said Monday. “Now it’s about preparing for Kansas City, what they do, what their schemes are, what their players are, what their tendencies are in certain coaching decision situations that we’ll have to make.”

The Chiefs are 4-5 and lost quarterback Matt Cassel to an injury to his throwing hand that Coach Todd Haley said could end his season. Tyler Palko played the last offensive series and was informed by quarterbacks coach Jim Zorn on Monday he’ll likely get his first NFL start against the Patriots.

That would scrap a meeting between Tom Brady and Cassel, his former backup who played unexpectedly well in 2008 after Brady suffered a season-ending knee injury in the opener.

Seems like an easy win for the Patriots, right?

Brady doesn’t think so, despite his team’s 6-3 record that puts it in sole possession of first place in the AFC East. The Patriots started Sunday tied with the Jets and Buffalo Bills, who both lost.

“There’s still a lot of football left to be played. Every team is still going to make improvements,” Brady said Monday on his contractually obligated appearance on WEEI radio. “And some teams are just going to continue to ride out the season and they can start thinking about next year.

“We want to be one of those teams that really starts building and getting better every week. I thought last night was a good step in the second half of the year. But obviously, the week starts again today. We’ve got to move on to the next game and start getting prepared for a team that we haven’t played in a few years.”

Going into Sunday’s games, the Patriots had the NFL’s lowest-ranked defense, a spot they’ve held most of the year. And they were without two key injured players, safety Patrick Chung and linebacker Brandon Spikes.

So safety Sterling Moore and linebacker Jeff Tarpinian got their first pro starts. Both were undrafted rookie free agents this year and Belichick had some concerns how they would perform in key roles.

“What happens when the lights go on, you never really know for sure,” he said. “You have to wait and see that. Jeff has been playing all year in the kicking game, so we’ve seen that. Sterling really hasn’t really had a lot of opportunity to play.”

Both did well, although cornerback Devin McCourty suffered a right shoulder injury when hit by Moore in the first half as both tried to tackle wide receiver Plaxico Burress.

Now they play six straight games against teams with losing records: Kansas City, at Philadelphia (3-6), Indianapolis (0-10), at Washington (3-6), at Denver (4-5) and Miami (2-7). They finish at home against Buffalo (5-4).

“It happens every week in the NFL,” Brady told WEEI. “You look up at the scoreboard during the game — or for us, because we played on Sunday night, we saw a lot of those games. And it’s like: ‘God, how did they lose?’ Or, ‘Wow, they beat so-and-so.’

“One team one week looks great, and then they play another team. Other than the Packers this year and the 49ers, you really don’t know what you’re getting every week.”