The Saints looked to be on the verge of a sixth consecutive victory before rookie free agent Kenbrell Thompkins outfought Greer in the end zone to catch a match-winning touchdown with just five seconds remaining.
Greer believes that his side showed good resilience during the contest despite the defeat, but admits that the play would weigh heavy on his mind until the next match.
"That's something that you'll replay in your mind for a long time," Greer told The AP.
"We fought hard, we're resilient, and it happens like that. For it to happen to me, I'll just have to bear the burden for this week."
The Saints still sit first in the NFC South despite the defeat, while the Patriots also top of the AFC East.