It was just after Lukaku had scored the game's only goal in the 20th minute that a majority of the travelling support broke into a chorus of the tune.
United contacted relevant bodies to see whether the song could be categorised as racism by the letter of the law, while saying once again in a statement following the game they have a "zero tolerance" to behaviour of this kind.
"I don't understand what the fans sing", he told a news conference when asked about the Lukaku incident.
Their latest victory was not routine as Southampton piled on the pressure in the second half, and United's Marouane Fellaini had to clear Oriol Romeu's header off the line.
After the Belgium global opened the scoring for the visitors, the Lukaku chant broke out in the stands with a defiant message at the end.
Following the 4-0 win over Everton on Sunday, the United manager said he does not know whether the France global will be out for "12 weeks or 12 days".
It was the fifth win of the Premier League season for both Manchester United and Manchester City which keep them at top of the points table, with Pep Guardiola's men only ahead of their rivals on goal difference.
"I know that last season, on these fixtures, I think we would have, maybe, five or six points less than we have this season", he said.
"But this is nothing".
The Saints got off to a promising start and went close after 11 minutes as Nathan Redmond volleyed just wide from close range. A hard period with an accumulation of matches that comes in October.
"We did that extremely well with a good goalkeeper, good defenders with Smalling and so I am really happy".
The Reds have been flying this season with 17 goals in 6 games so far and a near ideal win record with just 1 draw and 5 wins in total of 6 games. United are also expected to win by all 10 of our writers. "It's obvious. But it's not always possible".