McIlroy holed out from a bunker on the 18th to complete a closing 64, equalling the lowest final round in tournament history.
The 32-year-old finished three shots behind world number one Scottie Scheffler, who four-putted the 18th in an otherwise brilliant performance to claim his first major title with a fourth win in his last six starts.
“It’s what you dream about, right? You dream about getting yourself in position,” McIlroy said after his wild celebrations on the 18th green with playing partner Collin Morikawa, who also holed out from the same bunker.
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“I wasn’t quite close enough to the lead (but) to play as well as I did and then to finish like this, I mean, it’s just absolutely incredible.
“This tournament never ceases to amaze and that’s as happy as I’ve ever been on a golf course right there. That was an incredible. I’ve never heard roars like on the 18th green. It was really cool.
“I will come up a little bit short, but I gave it a great go and I can’t ask any more of myself. I went out there today, shot my best ever score at Augusta and it’s going to be my best finish ever.
“Probably not quite good enough, but I’ll come back next year and keep trying.”