McIlroy briefly held a two-shot lead with five holes to play at Pinehurst,
but bogeyed three of the last four, missing from two feet and six inches on the 16th and three feet and nine inches on the last to finish a shot behind Bryson DeChambeau.
The four-time major winner said earlier this week that Michael Jordan and Rafael Nadal had been among the sports stars to send him messages of support, with Woods doing likewise.
“I just sent him a nice text,” Woods said ahead of the 152nd Open Championship. “I waited a week before I sent it. I wanted to let it calm down.
I know he was being besieged by a lot of different things going on, and just let it cool down for a week.”
Asked what he had said in the message, Woods added: “Just basically, as you know, I’m your friend.
“I know this is a difficult moment.
“We’ve all been there as champions. We all lose.
“Unfortunately, it just happened and the raw emotion of it, it’s still there and it’s going to be there for, I’m sure, some time.
“The faster he’s able to get back on a horse and get back into contention, like he did last week (in the Scottish Open), the better it is for him.”
McIlroy admitted he felt uncomfortable over his par putt on the 16th, a feeling even a 15-time major winner like Woods could empathise with.
“Yes, absolutely. Nervous, shaky, uncomfortable, yeah, all of it,” Woods said. “That’s part of it. That’s why you love it. That’s why we practice, to build up ourselves in that one uncomfortable situation and bury it.
“I’ve missed plenty of putts. I’ve missed plenty of shots. Just like Jordan…you see all the game-winning shots, but also he’s missed a ton of game-winning shots too.
“The thing is you still take the game-winning shot and I still want the last putt.”
Asked what had been the hardest loss of his career, Woods picked out the 2009 US PGA Championship won by YE Yang. It was the first time Woods had failed to win a major when leading after 54 holes.
“That took a little bit of time to get over that because I had made some pretty stupid mistakes in the middle part of the round,” Woods said.
“I made a huge rally at the end, but too late. I made too many mistakes in the middle. You can’t afford to make the mistakes that I made and expect to win tournaments. I know better than that.”
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Source: USA Today