Rahm was bidding to become only the fourth player to retain a Masters title while McIlroy was making his 10th attempt at becoming only the sixth player to complete the career Grand Slam of golf's four major titles.
But McIlroy and Rahm, who respectively occupy the second and third spots in the official world golf rankings, were never able to get in the mix at the year's first major.
Rahm, who joined LIV Golf eight months after winning last year's Masters, squeaked inside the six-over par cut line but failed to make a move over the weekend and closed the major with a four-over-par 76 that left him at nine over on the week.
"There's a lot of things that contributed to me not having my best week, and one of them I think was obviously on the greens, which is not easy," said Rahm. "Never really had the pace of the greens, and a couple too many three-putts."
Making matters worse for Rahm, he was unable to quickly flee Augusta National and put the week behind him as Masters tradition requires the defending champion to present the Green Jacket to the next year's winner.
"It's been nice to have some receptions walking up to some tees no matter what my score was and seeing the appreciation," said Rahm. "But when you don't have your best week, it's not that - it's hard to have to stay now to put the jacket on somebody else and never really ever have a chance."
McIlroy, who began the day 10 strokes off the lead, opened his round with a bogey and then had a solid eagle opportunity at the par-five second but the Northern Irishman three-putted from eight feet for a disappointing par.
The four-times major winner rode two consecutive birdies into the turn but made bogeys at the 10th, where he failed to get up and down from a greenside bunker, and the par-five 13th, where he reached the green in two but four-putted from 73 feet.
McIlroy eventually posted a 72-hole total of four-over 292, his highest total score since the 2012 Masters.
"I'm close in some ways, but then I feel quite far away in others," McIlroy said of the state of his game. "It's a bit of a - once I get one thing, sort of put that to bed, then another thing pops up, and it's just one of those at the minute."
