Heung-min Son struck four times, with Harry Kane providing all four assists before scoring himself.
Mourinho said: “We didn't start bad at all. In the first 10 or 15 minutes we were good. After that we lost control.
"In the centre of our defensive area, we were a bit sloppy. We lost some duels. They got the ball behind us too easy. I was on the bench and thinking I would be happy to get in at 1-0.
“The goal gave us a different position in the game. In the second half, Harry Kane killed the game, the way he connected the game, the way he was dropping, he allowed Son Heung-min into attacking spaces. His performance was amazing.
“In the second half we were too good for them
“We know Southampton quite well - we played them four times last season, twice in the league and twice in the cup. [Former Southampton midfielder Pierre-Emile] Hojbjerg helped us to analyse and understand the way they play. We knew they risk a lot.
"The full-backs leave a lot of space behind. By Harry Kane's movement we killed them. He changed the game for me and of course Sonny."
On Dele Alli being left out, Mourinho explained, “It's too many [people in the squad]. When you bring 18 players you leave eight players behind. Not easy for Dele or any of them. Of course [he is still part of Spurs' plans]."
On new additions Gareth Bale and Sergio Reguilon, he added: “It's unfair for me to speak about new signings today when this team won 5-2. When Gareth and Sergio belong to the team and they are ready to play then they will be our players."