The Spaniard moved to St Mary's under controversial circumstances following the swift dismissal of Nigel Adkins, who remains out of work.
"You need to remember with the new manager that he is not involved in [the decision of] changing managers, he is just coming in to do his job," said Martinez.
"He was very impressive at Espanyol. He is well-organised, he has very clear football concepts and he is used to dealing with high-pressure games and with bringing youngsters through."
Pochettino was sacked from the Spanish club in November last year.