Scholes has been critical of Carrick's appointment and appeared to take a nasty swipe at the United manager after his first defeat at Newcastle last week.
In a deleted social media post, Scholes snapped: "Michael has definitely got something special about him...cos Utd have been (expletive) last four games."
However, on the The Good, The Bad & The Football podcast, Scholes insisted on Monday: "It was in no way intended to be offensive towards Michael.
"Michael is one of the nicest people you will ever meet in football, he'd be the last person that I would want to offend.
"I messaged Michael anyway. I went straight to Michael and said, 'Look, I was never intending to upset you'. And I don't think I needed to say that anyway and he told me himself he wasn't upset by it."
Scholes also said: "I think people have just taken it differently from what was meant.
"The only thing I was saying was that I don't think they played that well the last four games and he's still managing to get results.
"We had the greatest manager in the world and he always said sometimes you need a bit of luck. So with sending-offs and different things that happen through games, sometimes you do need a bit of luck, that's all I was saying."