Video footage showed Lukaku appearing to kick out at Bong following a tussle between the pair at the 66th-minute corner from which Ashley Young scored United's deflected winner in the 1-0 victory.
But Goal and Omnisport understand Lukaku will face no further action from the Football Association in relation to the incident after it was reviewed by three former match officials.
Each member of the panel would have had to agree the 24-year-old's actions were worthy of a sending off for further action to be taken and this was not the case.
If the Belgium international had been landed with a violent conduct charge, he would have been in line for a three-match ban to rule him out of the matches against Watford on Tuesday, Arsenal and Manchester City.
As it is, Lukaku is free to make his 200th Premier League appearance at Vicarage Road.
Lukaku has 12 goals for United in all competitions since joining from Everton for £75million in July but failed to find the net for the ninth time in 10 matches against Brighton.