Comparisons were made between McIlroy and Woods after the 22-year-old Northern Irishman swept to his first major victory in record-breaking style at Congressional on Sunday.
His status will undoubtedly soar as a result, but McIlroy said he'll try to stay grounded.
"With success comes expectation, and I know the expectation on me is going to be pretty high," McIlroy told Sky Sports TV on Wednesday. "I expect big things from myself, but as long as I can keep the commitment and dedication and put the hard work in, I don't see why there's any reason not to handle it OK."
McIlroy won the U.S. Open by an eight-shot margin, reviving memories of Woods' first major title -- a 12-shot victory at the Masters in 1997 at age 21.
Considering McIlroy had previously won just two tournaments in his professional career, it was a surprise how easily he handled the course and field over four days.
"Last week was fantastic, incredible," he said. "The golf I played, I'd never played before in my life. I just hope I can keep it going."
McIlroy returned to Britain on Tuesday and was back 24 hours later at his hometown club in Holywood, near Belfast, the course where he was groomed to be a star.
These are good times to be a golf fan in Northern Ireland -- 12 months ago, McIlroy's compatriot Graeme McDowell came back from the U.S. Open at Pebble Beach armed with a first major title.
McIlroy said McDowell's victory was inspirational.
"I remember going up to Portrush and seeing Graeme when he came back home, and it's nearly exactly a year later that I'm doing the same thing," McIlroy said. "What Graeme did last year at Pebble Beach definitely inspired me to go on and believe that I can win major championships, to follow in his footsteps and bring the trophy back to Northern Ireland.
"To think that no European had won it in 40 years before Graeme and then the two of us won it back to back. Growing up in tough (golf course) conditions, like the US Open usually is, probably helped us. But I don't think you can explain having two back-to-back U.S. Open winners from a country of 1½ million."
McIlroy is taking the next three weeks off. His first event back is the British Open at Royal St. George's in Sandwich, southeast England, starting July 14.