“I feel like we haven’t peaked yet . . . I feel like the sky’s the limit for this team,’’ Drew Brees said after throwing for three touchdowns in yesterday’s 38-7 rout of the struggling Tampa Bay Buccaneers.

“It only gets harder. By no means can we sit back on what we’ve accomplished thus far. Every team we face would love to give us that first loss.’’

The next opportunity goes to the Patriots, who haven’t made a regular-season visit to New Orleans since 1998, although they did win Super Bowl XXXVI over the Rams at the Superdome in 2002.

The Saints (10-0) shrugged off a slow start defensively, shutting down the Bucs after yielding a long touchdown drive to open the game. Offensively, they took advantage of numerous mistakes by young Tampa Bay quarterback Josh Freeman.

Robert Meacham caught touchdown passes of 4 and 6 yards in the first half, while Mike Bell scored on runs of 3 and 1 yards in the second, when New Orleans gained 147 of its 183 yards rushing.

A spate of turnovers made the Saints seem more vulnerable over the past month, but Brees didn’t throw an interception for the first time in five games. The Saints also didn’t allow a sack for the first time since Oct. 18 against the Giants.

“I like where we’re at. We’re 10-0 and we beat a division opponent on the road,’’ coach Sean Payton said. “I thought we got better today.’’

Brees said the NFL’s No. 1 offense can become even more efficient.

“The last four games, we kind of got back to some old habits that we didn’t want to, which was the turnovers and negative plays,’’ the quarterback said. “We needed a game like this, to come out and look sharp in all phases.’’

Tampa Bay (1-9) drove 95 yards for a touchdown on its first possession. But Freeman had little success after his 18-yard scoring pass to Michael Clayton gave the Bucs a short-lived 7-0 lead.

Brees countered that score with a 68-yard drive that Meacham finished with his 4-yard scoring reception.

Malcolm Jenkins’s interception and 14-yard return to the Tampa Bay 29 set up John Carney’s 38-yard field goal for a 10-7 lead. Poor clock management by the Bucs at the end of the second quarter gave Brees an opportunity to put another touchdown on the board to make it 17-7 at the half.

Brees was 19 of 29 for 187 yards before being replaced by Mark Brunell late in the fourth. With Reggie Bush out with a knee injury, Pierre Thomas rushed for 92 yards on 11 carries and Bell contributed 75 yards on 13 attempts.