The two Spurs players had to be separated when they left the pitch in the half after goalkeeper Lloris had criticized Son for not doing his defensive work.
An incensed cry pushed the South Korean international when the players left the field of play, and the teammates had to throw Son down the tunnel.
Then the couple showed up for the second half seeming to have settled their differences and hugged each other on the whistle full time.
“It’s beautiful,” Mourinho said after the match. “If you want to blame someone for that, it’s me, because I was critical of my guys, because they’re not critical enough of themselves, of each other.
“It’s a very important thing for the team to grow and that’s why we need to demand each other and be strong personalities.
“A team of nice guys, the only thing they can win is the Fair Play Cup, something I never won and I’m not interested in.”
A strong own goal from defender Michael Keane was enough to give Tottenham the win over Everton in such a disastrous match at Tottenham Hotspur Stadium.
The Spurs, who came from a 3-1 defeat to Sheffield United, are now in the round of 16 to call for a delay for European football next season.
French international Lloris said the incident with Son was “part of football” and said they had continued.
“There is no problem. There is a lot of respect between him and me,” he told BBC Sport after the match.