A number of the visiting supporters reprised the song after the Belgium international scored what proved to be the only goal of the game after 20 minutes at St. Mary's Stadium.
A chorus of, "We're Man United, we'll sing what we want" followed, in clear defiance of pleas from Lukaku and the club not to sing a song described by anti-discrimination group Kick It Out as "offensive".
Mourinho said he doesn't hear lyrics of fans' songs during games – with the exception of a simple vitriolic chant often aimed at him by opposition fans – but he praised the United contingent for helping his side to battle to a 1-0 win.
"I don't understand what the fans sing," he told a news conference when asked about the Lukaku incident. "The only music I understand clearly is one from my opponents when they tell Mourinho to go to a place. That's the only one I understand.
"But the only thing I will say is the fans were amazing, the support amazing from the first to the last minute. It's important to have that, not when you're winning 3-0 or 4-0 and winning the game, but it's more important when you are defending and are exhausted.
"The songs? I don't understand them."
Mourinho was sent to the stands by referee Craig Pawson in second-half injury time after he had been summoned to the touchline by fourth official Mike Jones, but the reason remains a mystery to the United boss.
"I don't know [what happened]," he said. "Craig told me to leave, and I left."
Mourinho feels it was a victory they might not have managed last season but admitted he would prefer to win matches by a healthier margin.
"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. "So we are better this season than last.
"But this is nothing. It's just a start. A difficult period with an accumulation of matches that comes in October. I really think that six teams are going to fight for the title.
"It's better to win 5-0 than 1-0. We wanted to win also 5-0. It's obvious. But it's not always possible."