McIlroy managed just two birdies in wet and overcast conditions at the Carton House course on the outskirts of Dublin.
It left the world's No. 2-ranked golfer trailing eight shots behind leader Oscar Floren of Sweden, who capped his 6-under 66 by driving the green at the par-4 13th and holing a 20-foot eagle putt.
"I just came out and hit everything really, really pure," Floren said.
Five players were tied for second after 67s: Dutchman Joost Luiten, American Peter Uihlein, Frenchman Jean-Baptiste Gonnet, Northern Ireland's Michael Hoey and 2009 winner Shane Lowry of Ireland, who was grouped with McIlroy.
Thomas Bjorn of Denmark, the 2006 champ the last time the Open was at Carton House, was among six players who carded 68s.
McIlroy hit just five of 14 fairways, and took 34 putts.
"At the moment, no aspects of my game are strong and I'm just feeling a bit lost at the moment," he said.
"It feels good on the range and I can hit all the shots but when I get out on the course it really does not seem to be there.
"Off the tee, I am missing one right and then missing one left and it's just not going where I want it. It gets you in two minds every time you are playing a tee shot.
"The game is just not coming easy to me at the moment and while I was struggling at this point last year, I was able to turn the corner in the middle of the summer and have a great end to my season.
"I don't know whether it's a matter of trying to play my way out of it or just keep grinding away on the range or whatever."
Lowry captured the Irish Open as an amateur four years ago, when McIlroy tied for 50th. Earlier this year, Lowry also humbled his good friend McIlory in bundling him out of the opening round of the Accenture Match Play Championship in Arizona.
Now he has again upstaged McIlroy in a display that included six birdies and just one bogey.
"I was just chomping at the bit to get out there this morning and I was just trying to play me way into the tournament nicely so I'm really pleased with a 67," he said.
Hoey revealed his wife, Barbara, had their first child induced last week so he could compete in the Open.
"It's great being a father and already it's added a new perspective to my life," said Hoey, a four-time European Tour winner.