Lloris pushed Son after the half-time whistle, with both players not backing down before being separated by their teammates.
Spurs would win the match 1-0, and Mourinho was pleased to see his players show some passion when speaking after the game.
The pair kissed and made up at full-time after sealing all three points.
He said: "It's beautiful. It's probably as a consequence of our meetings. If you want to blame someone for that it's me. I was critical of my boys - they were not critical enough with themselves. I asked them to be more demanding of each other.
"Son is an amazing kid, everybody likes Son but the captain told him you have to do more and give more to the team.
"It's something needed for the team to grow up - to grow up you need big personalities. When you have that reaction I had no doubts."
Hugo Lloris & Son clashing with each other at half-time pic.twitter.com/jjVeKy36AR
— Football Daily (@footballdaily) July 6, 2020
Lloris & Son at full-time hugging it out after they clashed at HT. pic.twitter.com/JB5NHcCJi6
— The Spurs Web (@thespursweb) July 6, 2020