Monk accused Stoke winger Moses of cheating to win a penalty in a 2-1 Premier League defeat at the Britannia Stadium on October 19, a remark that drew the ire of opposite number Mark Hughes.
The Football Association (FA) announced in the aftermath that they had contacted Monk in order to "seek his observations" over the comments, but have now drawn a line under the matter according to Swansea.
"The FA has reminded the Swansea manager about his responsibilities regarding media comments," read a statement on the club's website.
The Moses incident was a tipping point for Monk, who felt that Swansea had been on the receiving end of a number of poor refereeing decisions since the start of the season.
The 35-year-old is reportedly set to meet referees' chief Mike Riley on Friday to discuss the matter and will have yet more to talk about following Swansea's controversial elimination from the League Cup at the hands of Liverpool on Tuesday.
Having seen Mario Balotelli come off the bench to cancel out Marvin Emnes' earlier opener, Swansea had Federico Fernandez sent off in stoppage time for what looked like a perfectly legal challenge on Philippe Coutinho.
Dejan Lovren scored a last-gasp winner to send Swansea out of the competition they won in 2013 and the Welsh club have since appealed the dismissal.
