Rams’ floundering defense will have its hands full against Tom Brady and the Patriots

New Orleans quarterback Drew Brees dropped back from the Rams’ 21-yard line in the third quarter last Sunday and lofted a pass to Michael Thomas, who easily beat defensive back E.J. Gaines on a corner route toward the left sideline.

Thomas made the catch at the eight-yard line, where Rams safety Maurice Alexander closed but couldn’t wrap up the receiver or knock him out of bounds. Gaines caught Thomas from behind near the two, but realizing he couldn’t haul the receiver down, he shoved Thomas into the end zone in disgust.

The score was the sixth of seven touchdowns for the Saints in a 49-21 victory, the Rams’ sixth loss in seven games, and it encapsulated much of what ails a defense that suddenly has gone soft after being dominant for almost 10 games:

Poor coverage. Missed tackle. Anger and frustration. About all that was missing was a penalty.

“We should have played for free the way we got our ass kicked,” defensive end William Hayes said this week. “Giving up seven touchdowns and letting them have their way with us … that’s not how our defense is. It’s just embarrassing all the way around.”

The Rams (4-7) have played 44 quarters this season, and for 39 1/2 of those, their defense was among the NFL’s best.

But in the last 4 1/2 quarters — the final two drives of a 14-10 loss to Miami in the Coliseum on Nov. 20 and the loss to the Saints in the Mercedes-Benz Superdome — the Rams have allowed 475 yards passing and seven touchdowns on 41 of 50 attempts and 216 yards rushing and two touchdowns on 34 carries.

To put those numbers into perspective, the Rams have allowed 19% of their passing yards and 17.5% of their rushing yards on the season in the past 4 1/2 quarters. They’ve allowed nine touchdowns on their last 15 drives after giving up 19 touchdowns on their first 114 drives.

The 555 total yards allowed in New Orleans were the third-most in the Rams’ 80-year history.

“Those numbers are not acceptable, and we have to get better,” cornerback Trumaine Johnson said. “We have to start locking up, especially at the end of the game, when it’s grind time.”

Some reasons for the slippage are obvious. While a line led by tackles Aaron Donald and Michael Brockers has remained solid — the Rams sacked Brees twice and had six other hits — the secondary has been burned repeatedly, and linebackers have yielded some big plays to tight ends.

Gaines has been a weak link at corner — he’s the only Rams defender whose play is rated as “poor” by Pro Football Focus — and the loss of cornerback Troy Hill, who was waived after a Nov. 19 DUI arrest and subsequently signed to the practice squad, has thinned secondary depth.

Some of the issues are not so obvious.

“This past game, we didn’t get lined up correctly most of the time,” said linebacker Alec Ogletree, who is responsible for making defensive calls. “We just had a lot of mistakes on defense, and it cost us. Some of it was communication, some of it is not sticking to the game plan.”

In part because of those alignment problems, “we just didn’t play gap-sound football,” Hayes said. “We didn’t really play disciplined, and they did a good job of scheming us up.”

The mistakes were addressed in the film room, “and now we’re moving on from it,” Donald said. “It’s gonna be fixed, and it’s not gonna happen again.”

Said Ogletree of Sunday’s game at New England: “We’ll definitely come out ready to play.”

But a game against Patriots quarterback Tom Brady, one of the NFL’s premier passers for almost two decades, could be another recipe for disaster for the Rams. Brady, 39, has an NFL-best quarterback rating of 116.7 and has thrown for an average of 314 yards in seven games, with 18 touchdown passes and one interception in 256 attempts.

He has a deep and versatile pass-catching fleet, but it will have to absorb the loss of tight end Rob Gronkowski, who reportedly will undergo back surgery on Friday in Los Angeles.

Julian Edelman is one of football’s best possession receivers, with a team-leading 64 catches for 617 yards. James White is a threat out of the backfield, with 43 receptions for 375 yards, and Chris Hogan (23 catches for 461 yards) and Martellus Bennett (42 catches for 540 yard) are big-play threats.

New England ranks sixth in the NFL in points (26.6), offense (286.2 yards) and passing offense (270.4) a game, and seventh in rushing (115.8) behind LeGarrette Blount (212 carries, 869 yards, 12 touchdowns).

“Tom Brady will go down in history as one of the best quarterbacks in the league,” Rams cornerback Lamarcus Joyner said. “When you have a quarterback who can make the guys around him just as good as he is, then you have to play disciplined, sound football.”

It all starts up front. For the Rams to compete with the Patriots, they’ll have to pressure Brady, much like Denver did in last January’s 20-18 win in the AFC championship game, when they sacked Brady three times and had 14 additional hits.

“Any time you put pressure on the quarterback or hit him and get sacks, you can make him frustrated, no matter how good he is,” Donald said. “If we can do that, it will make their job harder and the job of our guys in the back end easier.”

mike.digiovanna@latimes.com

Twitter: @MikeDiGiovanna