The Red Devils sit atop the fledgling league table after two emphatic 4-0 wins against West Ham United and Swansea City.
Although Mourinho is happy about United hitting the ground running this season, he also acknowledged how their similarly good start last year was not built upon.
The Portuguese coach told Sky Sports News: "The thing I want to happen is for the team to be losing. So I can see the way we react emotionally.
"At this moment, everything is going in our favour, but it is not always going to be a motorway. You can always find difficult journeys and road blocks, and we have to be ready for that.
"It has not happened so far but going a goal behind will be a different challenge and I want to see how these players try to change a result. Let's see how we are when we are in difficulties, when we need the last minutes to win matches.
"Of course I am happy with the way we have started the season. And the quality of our performances has given me even more confidence. But I don't forget that we started last season with six points from our first two matches and still finished sixth."
Up next for United is a home encounter against former Premier League champions Leicester City next Saturday.