The Argentina icon – who has rarely been out of the headlines during Russia 2018 – claimed Colombia were victims of a "monumental theft" and laid into the performance of the officials.
England had been awarded a second-half penalty for a foul by Carlos Sanchez on Harry Kane – a decision that drew the particular ire of Maradona.
Fifa responded and described the 57-year-old's comments as "entirely inappropriate and completely unfounded".
But Maradona has now moved to make peace with world football's governing body by stressing that he simply got carried away in the moment.
"Taken by the thrill of cheering for Colombia the other day, I said a few things and, I admit, some of them are unacceptable," he wrote on Instagram. "My apologies to Fifa and its president.
"However much that sometimes I may have opinions contrary to some refereeing decisions, I have absolute respect for the work – not easy – that the institution and the referees do."
