The Argentina legend had landed himself in hot water with FIFA over his outburst at US official Mark Geiger when he described England's win on Tuesday as a "monumental robbery".
But after a firm rebuke by football's governing body the 1986 World Cup winner issued a mea culpa on Instagram.
"Caught up by the excitement and support for Colombia the other day, I said some things that, I admit, are unacceptable.
"My apologies to FIFA and its president (Gianni Infantino): even if sometimes my opinions are different to those of the referees I have total respect for their work."
He admitted that "although I sometimes have opinions contrary to those of referees, I have absolute respect for the work -- not easy -- which (FIFA) and the referees do."
Maradona, who had come out in support of Colombia following Argentina's premature elimination, blamed Geiger for the South American side's loss in an ill-tempered affair.
He had told Venezuelan TV channel Telesur: "I apologise to all the Colombian people, but the players are not to blame.
"Here is a gentleman (FIFA referees boss Pierluigi Collina) who decides to choose a referee who, if he had Googled him, (he would know) can't be used for a match of this magnitude."
Geiger was suspended from international football for six months after several controversial decisions during a 2015 Gold Cup semi-final between Panama and Mexico.
Maradona had attended the Colombia v England match as a guest of FIFA and was pictured before the game in Moscow wearing a Colombia shirt.
FIFA had responded, saying it was "extremely sorry" to read the comments from "a player who has written the history of our game".
It added: "Furthermore, it also considers the additional comments and insinuations made as being entirely inappropriate and completely unfounded."