Romelu Lukaku gave United the lead after 20 minutes with his sixth goal of the season but struggled to match their fine performances which have inspired their positive start to the season as Southampton improved as the match went on.
The fact that the Saints failed to score was as much down to the hosts' long-term struggles in front of goal as the impressive form of Bailly and Jones, which will come as a welcome change for United after years of defensive instability since the departures of Rio Ferdinand and Nemanja Vidic.
When Mourinho was asked about his defenders' performances, he said: 'Very good. And also (substitute Chris) Smalling.
"We did for 20 minutes what the majority of the Premier League teams are doing, which is to play defensively with five at the back.
"We did that for 20 minutes. We had chances to kill the game and score the second goal, but didn't.
"Then, Southampton were strong. I felt the manager (Mauricio Pellegrino) enthusiastic, exciting, risking bringing on two strikers like (Manolo) Gabbiadini and (Charlie) Austin to play direct, and also in a style that isn't normally their style."
This narrow victory had a significantly closer scoreline than United's four previous Premier League victories and Mourinho said: "It's better to win 5-0 than 1-0. We wanted to win also 5-0.
"But it's not always possible. We had opportunities in the first half to score the second goal and then the game is different.
"Lukaku and (Ander) Herrera, too, and if we'd done that I would have brought on (Anthony) Martial and (Jesse) Lingard and go for a different result. But credit to Southampton and to Pellegrino."