Mr Trump invited the County Down golfer to play at his Trump International Golf Club on Sunday.
After 18 holes on the Florida course, McIlroy said of his playing partner: "He probably shot around 80. He's a decent player for a guy in his 70s."
However, following a backlash on social media, McIlroy took to Twitter on Friday evening to defend his actions.
In the post, he said he respects Mr Trump's office and hit out at those who described him as a fascist and a bigot in the wake of the meeting.
"I don't agree with everything my friends or family say or do, but I still play golf with them," he tweeted.
"Last week, I was invited to play golf with the president of the United States. Whether you respect the person who holds the position or not, you respect the office that he holds."
He added that the game was "not an endorsement, nor a political statement of any kind".
"It was, quite simply, a round of golf," he wrote.
"I've travelled all over the world and have been fortunate enough to befriend people from many different countries, beliefs and cultures.
"To be called a fascist and a bigot by some people because I spent time in someone's company is just ridiculous. I hope, to some degree, this clarifies my decision to accept the invitation."

The BFI praised the 46-year-old's "mesmerising screen presence" which "has captivated audiences since her earliest roles".
The actress won Academy Awards for her roles in Woody Allen's Blue Jasmine in 2014 and in 2005 for The Aviator.
She will be awarded the honour at the London Film Festival's annual awards ceremony on 17 October.
The BFI described Blanchett as "a fearless and subtle actress".
"She has the rare gift of seeming utterly to inhabit the characters she plays and has an amazing ability to convey complex layers of emotion to stunning effect," it added.
Blanchett shot to global fame playing Queen Elizabeth I in 1998 film Elizabeth, followed by roles in The Talented Mr Ripley, The Lord of the Rings trilogy and The Curious Case of Benjamin Button.
The actress has two films receiving their UK premiere at the London Film Festival - Carol and Truth.
Truth, which also stars Robert Redford and Mad Men's Elisabeth Moss, tells the true story of CBS journalist and 60 Minutes producer Mary Mapes, who risked her career to find the "truth" and expose a story on the then US President George W Bush.
It will be screened as the Fellowship special presentation film.
Set in 1950s Manhattan, Carol sees Blanchett play a woman trapped in a loveless marriage who falls for a younger woman, played by Rooney Mara.
Previous recipients of the Fellowship include Tim Burton, Helena Bonham Carter, Ralph Fiennes and Stephen Frears.
Al Pacino and Mel Brooks have also been awarded the honour in the past year.
Suffragette, starring Meryl Streep and Carey Mulligan, will open the London Film Festival on 7 October, while Danny Boyle's Steve Jobs biopic will bring it to a close on 18 October.

The Portugal left-back struggled for first-team football at the Spanish club last season.
Former Manchester United manager David Moyes tried to bring him to Old Trafford in September 2013 but a transfer deadline day loan move fell through.
The 27-year-old joined Real from Benfica for a reported £25m in 2011.
Find all the latest football transfers on our dedicated page.

Local man, Joe McMinn, 28, was discovered in an area known as Devil's Den, near Goodwyns housing estate in Dorking, in the early hours of Easter Monday.
Richard Taylor, 21, of no fixed address, is due to appear at Guildford Magistrates Court later.
A post-mortem found Mr McMinn died of multiple stab wounds.
Rory McIlroy has said a round of golf he played with Donald Trump was not an endorsement of the US president.
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Oscar-winning actress Cate Blachett is to receive the BFI Fellowship for her contribution to film.
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Real Madrid defender Fabio Coentrao has joined French side Monaco on a season-long loan deal.
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A man has been charged with murder after a body was found in a woodland stream in Surrey.