Saints should have gone ahead within five minutes when Eric Bailly was adjudged to have handled in the area, but United goalkeeper Romero saved Manolo Gabbiadini’s penalty.
Bailly’s sharp shot was stopped by Fraser Forster, as the United defender created his side’s best chance of the first half.
Southampton forced Romero to make multiple blocks after the break while Anthony Martial hit the post from 25 yards for the visitors.
With Jose Mourinho’s side guaranteed a sixth-place finish before kick-off and one eye firmly on next Wednesday’s Europa League final, it always looked like being a sedate affair on the south coast and that is how it turned out.