Lukaku, who cost the Red Devils £75m to sign from Everton in the summer, became just the second United player to score six goals in his first six Premier League appearances when finding the net at St Mary's Stadium.
All in all Lukaku has eight in eight for United, the latest of which proved to be the winner in the tight affair with Southampton, and Mourinho admits that he has been left surprised by the Belgian's early-season form.
"I knew that he would always score goals. I knew that he would score more goals for us than for Everton or West Bromwich Albion, that's logic," he told BBC Sport. "But I was not expecting him to be match after match putting the ball in the net."
As well as scoring six times in the Premier League, Lukaku has also netted in the UEFA Super Cup and Champions League in the opening two months of the campaign.