The United forward appeared to petulantly kick out at Bong just prior to the hosts scoring the only goal game midway through the second half when Ashley Young's shot took a wicked deflection off Lewis Dunk and flew into the far top corner.
Former Premier League referee Graham Poll said Lukaku should receive a three-game ban for the incident but The FA have decided Lukaku will face no further action.
The incident was referred to three former Premier League referees to review. All three had to agree it was a sending-off offence for action to be taken and that was not the case.
Speaking to the Daily Mail, Poll said: "Manchester United striker Romelu Lukaku must face a three-match ban once the FA view replays of the incident between the Belgian and Brighton’s Gaetan Bong just before the only goal of the game.
"The incident started with the usual jostling between players at a corner but turned into a much more serious clash.
"Lukaku was impeded as the corner came in but his reaction was extreme, kicking out first with his right foot and then making full contact with his left foot somewhere quite painful. It was a violent act which would have resulted in a red card had referee Neil Swarbrick seen it. The Brighton full back did remarkably well to not react, nor complain to the officials. He deserves praise for that.
"Later in the second half, Swarbrick did see the challenge by Shane Duffy on Zlatan Ibrahimovic but failed to punish it correctly.
"Duffy flew into a tackle in the 87th minute with studs first and at pace, wiping out the Swede, who could have been seriously injured.
"It was also a red-card offence but, as Swarbrick punished it with a yellow card at the time, the FA cannot act.
"United manager Jose Mourinho will be understandably irritated if Lukaku is banned retrospectively after Duffy escaped, but he should take comfort in the three points because the only goal of the game — Ashley Young’s deflected effort — came just after the whistle should have blown for Lukaku’s assault."
Albion were frustrated earlier this season when striker Tomer Hemed was retrospectively banned for three games following an incident with DeAndre Yedlin in the 1-0 win against Newcastle.