McIlroy shot a mediocre 71 to slip eight strokes from the lead in an event he is only playing as part of a deal he made with the PGA Tour to play an exhibition in Turkey three years ago.
He said he would use the final round to hone his game for the upcoming stretch on the European Tour.
"It was another one of those days that nothing really went for me, I just couldn't get anything going, got a little frustrated," McIlroy told reporters.
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"I'm going to try and play a good round tomorrow, but one eye on this and one eye further down the road.
"I'm looking at the three tournaments I've got coming up, which are important to me because I want to try to win the Race to Dubai again."
He also had a narrow escape when he was almost struck by Argentine Emiliano Grillo's tee shot.
McIlroy had just played a chip shot from next to the green at the driveable par-four 17th when Grillo's drive landed only a couple of feet from the surprised the Briton, who clearly received no warning.
European Ryder Cup team mate Rose had a better day.
"Today was a test of patience," the 2013 U.S. Open champion said after a bogey-free round.
"I think I did the bare minimum required to keep believing and give myself a good chance tomorrow. It's going to take something pretty good to pull through and win."
Steele, seeking a second PGA Tour win, started the day with a two-shot lead but could not extend his advantage despite the benign conditions.
"I'm really happy with the state of my game all the way through the bag," the 32-year-old, who was raised in a small town in the southern California mountains, told PGA Tour Radio.
Loupe picked up shots early and late en route to the best round of the day and a share of the course record in the opening event of the 2015-16 PGA Tour season.
He birdied the first five and the last four holes to move within sight of his maiden tour victory. He has never finished better than fourth on the Tour.
South Korean-born Na is seeking his second tour win after several near-misses since his lone triumph in 2011.
He jumped into contention with a six-foot eagle at the par-five 16th, and added a tap-in birdie at the last.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Peter Rutherford/John O'Brien)
