The 54-year-old was sent to the stands by referee Craig Pawson for encroaching on the pitch during stoppage time of his side's 1-0 win at St Mary's on Saturday.
Unlike players, there are no automatic bans for red- carded managers and any additional punishment depends on the referee's report.
In this case, Mourinho appears to have taken the referee's decision without any further comment or reaction and the matter is closed.
The United boss said after the match that he was baffled by his red card. "I don't know," he said. "Craig told me to leave, and I left."
The club are understood to be liaising with Southampton to gain access to CCTV footage of Saturday's crowd so it can identify those responsible.
United reiterated their condemnation of the crude chant about Lukaku. Both United and Belgian striker Lukaku had previously implored supporters to stop singing the song, which draws on racial stereotypes about the size of black men's penises.
But fans sang it again at St Mary's, as well as "We're Man United, we'll sing what we want".
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