The world number four and Elkington engaged in a public spat on Twitter after McIlroy missed the cut at the US Open for the second year running.
The Australian said McIlroy, having won four majors and with "100mill in bank", was bored playing without Tiger Woods.
McIlroy responded with: "More like 200mill, not bad for a 'bored' 28-year-old. Plenty more where that came from."
Speaking on the eve of his defence of the Irish Open at Portstewart, McIlroy revealed he regretted reacting to Elkington and was avoiding social media for the foreseeable future.
"I must have wrote that tweet and deleted it about five times before I actually sent it," McIlroy said on Wednesday.
"I sort of regret sending it at the end but I actually gave my wife, Erica, my phone and my Twitter and told her, 'Change my password to something else and don't tell me what it is'.
"So as of the time being, I'm off social media just because of that reason. I don't need to read it. It's stuff that shouldn't get to you and sometimes it does.
"It is not what was said. It was who said it and anyone who has been in that environment should realise how hard golf is at times. That is the thing that got to me more than anything else.
"If it was written by a member of the media or something I could let it slide, because I can sort of say to myself, they don't really know how it is and they don't know what you have to deal with.
"But a former player that has won a major and been successful, that's sort of why it got to me and that's why I sort of retaliated a little bit."
McIlroy has recorded five top-10 finishes in majors since his last victory in the 2014 US PGA without seriously contending, but is optimistic about adding to his tally despite an injury-hit campaign with The Open Championship at Birkdale at the end of July.
"I am close," the Northern Irishman added. "I have got two big opportunities coming up this summer.
"Birkdale is a golf course I feel I can do well at. Then Quail Hollow for the PGA, I have won there two times, my first win on the PGA Tour and last time I won by seven.
"I think they are two opportunities for me to get back on the major ladder and start to win those again."
After missing the cut in the Irish Open for three years running, McIlroy won the title at the K Club 12 months ago.
And he believes he has learnt how to handle all the off-course distractions which come with his charity, the Rory Foundation, being the tournament hosts.
Rory McIlroy says he has stopped using social media following his row with former US PGA champion Steve Elkington.