Beckham finished with five catches for 44 yards, including a long of 16.
Safety J.J. Wilcox used a crushing hit on Beckham with three minutes left in the first quarter to break up an apparent completion. The hit sent Beckham to the sideline briefly.
Wilcox broke his nose on the play.
“I knew that I had to bring my A-game every time I was lined up close to him,” Wilcox said. “Hopefully, I succeeded in that."
Beckham caught two passes for eight yards against Carr and one pass for 16 yards against Patmon when he was lined up in the slot.
He caught one pass each against Wilcox and rookie Byron Jones.
"We did a lot of man coverage in the game,” coach Jason Garrett said, "and those guys did a good job neutralizing him. Obviously, he's a really good receiver."
Although Beckham missed last season’s first four games, he finished with 91 catches for 1,305 and 12 touchdowns.
He had seven 100-yard games, including six of 130 yards or more. He caught at least seven passes in eight of nine games.
Beckham’s 44 yards receiving was his lowest output since a four-catch, 34-yard performance against the Cowboys in Week 7 last year.
"We challenged our guys throughout the ballgame -- sometimes in single coverage, sometimes when they had a little bit of help,” Garrett said, "but for the most part they did a good job slowing those guys down."