Woods, 42, a 14-time Major winner, briefly held the lead at Carnoustie before finishing five under and three shots back of winner Francesco Molinari, who became the first Italian to win a Major in golfing history.
The Northern Irishman, who himself finished a shot ahead of Woods in a four-way tie for second behind Molinari, claims he sees a 'different version' of the man who tormented his fellow players in the early 2000s.
Asked if he would be happy to deal with Woods for a few more years, McIlroy said: "Yeah. I mean, not Tiger that Phil (Mickelson) and Ernie (Els) and those guys had to deal with. It's a different version.
"But he's right there, he's getting himself in the mix. He looked good in D.C. a couple of weeks back, he's looked good here.
"I'm not sure if that finish is going to get him into Akron or not. He's played a full schedule, he's healthy, I wouldn't say we're worried about him but he's one of those guys that's always in with a shot."
Woods has not added to his 14 Majors since the US Open, but has surged back into contention after recovering from four back surgeries since 2014.
For a short time he led the 147th Open, the first time he has done so at a Major since 2013, but McIlroy was relieved to see him relinquish his position.
Agreeing that Woods is now beatable from winning positions where before it was a foregone conclusion, McIlroy said: "With the Tiger we have to face, he does things that maybe he didn't do ten, 15 years ago.
"But it's still great to have him back, it's still great for golf. It will be interesting to see going forward, but this was his first taste of a major championship for a while.
"Even though he's won 14, you have to learn how to get back, I'm relearning.
"I feel like I've won quite a few recently, but you still have to relearn to deal with it.
"Today was a good day for both of us with that, I guess."
McIlroy is himself riding a three-year streak without a Major after his 2014 PGA Championship triumph.