Saints fans aimed chants at the Spurs boss throughout their clash on Sunday afternoon.
Pochettino's Tottenham Hotspur side were hosting Koeman's men at White Hart Lane and managed to secure a 1-0 win against them.
But Saints fans aimed chants and taunts at the Spurs boss throughout the game, relating to Pochettino's decision to swap Southampton for north London this summer.
And Koeman has voiced his disapproval at the supporters' behaviour, saying he respects his Argentine counterpart 'very much.'
"Yes, okay that is the reaction of the fans and I don't agree with that," Koeman told reporters.
"I think everybody needs respect and normally the respect is high in the Premier League.
"I respect Mauricio very much and he did a great job in Southampton. Now he is the manager of Tottenham and it is a great challenge for him."
Pochettino, however, says he still loves the Southampton faithful:
"I still love Southampton and maybe I can understand but this is football," he said. "I do not change my feeling, nothing about Southampton.
"For me it was a great moment, a great period of 18 months and always I will be grateful to Southampton Football Club and the people in Southampton."