The rookie believes there are more great catches to come, including some he can make and celebrate.
"I haven't really seen it yet. I saw it on the replays," said Beckham, who finished with 10 catches for 146 yards and two touchdowns in the 31-28 loss to the Dallas Cowboys.
"I hope it is not the greatest catch because with time I hope I can make more. It really means nothing. You still go home at the end of the day with a loss, and that's just not a good feeling."
The catch lifted a sellout crowd of more than 80,000 fans out of their seats, and it didn't make a difference if they were rooting for the Giants (3-8) or the Cowboys (8-3).
Players on both sides couldn't say enough and fans flooded the internet with comments about Beckham's catch,
"Man I just witnessed the greatest catch ever possibly by Odell Beckham Jr! WOW!!!!" LeBron James tweeted.
Beckham's right hand was fully extended in almost a backstroke motion while his legs were almost perpendicular to the field.
"It's special," Dallas quarterback Tony Romo said. "I've got a guy on our team who makes come incredible catches. That one is right there with anything I've ever seen. That was pretty impressive."
Beckham, who missed the first four games of the season, agreed it was his best in a game — for now.
"I guess I have to thank my mom for the long fingers," said Beckham, who practices one-hand catches before every game. "Hers are maybe a half an inch shorter than mine."
Still, it wasn't enough to prevent the Giants from losing their sixth straight game, as Romo led a game-winning drive after New York took a 28-21 lead on a 1-yard touchdown pass from Eli Manning to Adrien Robinson with 3 minutes to play.
Romo threw two touchdown passes to Dez Bryant, the game winner coming from 13 yards with 1:01 remaining. It capped an 80-yard march in which Romo never was pressured as he searched for receivers.
Dallas, which was treated to chants of "Let's Go Cowboys!" in the second half from hundreds of fans in Cowboys garb, is 5-0 on the road. New York, meanwhile, was eliminated from division contention.
Thanks to Beckham's catch, one of the rookie's two first-half touchdowns, New York built a 21-10 halftime lead.
But Romo hit Cole Beasley with a short pass that he turned into a 45-yard score, and the quarterback's 31-yarder to an uncovered Bryant put Dallas on top for the first time.
Beckham left briefly in the fourth quarter with a back problem, but returned for the next series. He wasn't involved in any key plays on that TD drive to retake the lead, and Beckham finished with 10 receptions for 146 yards.
"Hopefully, it's a bruise," Beckham said.
League rushing leader DeMarco Murray managed his 10th 100-yard game this season with 121 on 24 carries for Dallas.
Beckham's right-handed stab of Manning's 43-yard rainbow pass could be the catch of the year. The rookie, who regularly practices such receptions, outreached veteran cornerback Brandon Carr at the goal line and tumbled backward into the end zone to make it 14-3.
"I have seen him make catches like that all the time (in practice)," coach Tom Coughlin said.
That catch already was dominating highlight reels by halftime and was his second TD of the game. The 80-yard drive to Beckham's first touchdown marked the second straight week the Giants got into the end zone on their opening possession after going 20 games without doing so.
Dallas' offense hardly was in awe following Beckham's one-hander. Romo guided the Cowboys 77 yards and used a shovel pass to Jason Witten — yes, the tight end used two hands — from the 4 immediately after Beckham's stunner.
So the kid from LSU went right back to overwhelming the Cowboys. He made three catches for 32 yards on New York's next series, including a spin move that would make a figure skater proud. Andre Williams concluded that 80-yard march with a 3-yard run for a 21-10 lead.
In the first half alone, Beckham had eight catches for 125 yards, while Manning went 14 of 16 for 191 yards. But the second half belonged to Dallas.
NOTES: Manning threw five interceptions last week in a loss to San Francisco, but Church's pick was the only one Sunday night. He finished 29 for 40 for 338 yards. ... Murray has rushed for 1,354 yards. ... Romo was 18 of 26 for 275 yards and never appeared bothered by back problems that sidelined him for one of the Cowboys' defeats this year.