The Argentine led Southampton to eighth in the Premier League table last season and Rodriguez accepts that Pochettino’s departure is ‘just one of those things that can happen in football.’
The 24-year-old Burnley-born striker said: "Mauricio is a great manager and a great guy and was well-respected by the lads.
"He worked us really hard and we got the good results and finished eighth which we were happy with. Football moves on though so it's just one of those things."
Saints have also lost Rickie Lambert who heads back to the city of his birth – Liverpool – after spending almost five years at the club.
Adam Lallana, Luke Shaw and Calum Chambers are other Southampton players linked with moves away from the south coast but Rodriguez is not overly concerned.
He added: "You don't want to see players going and the team being taken apart.
"But you can never stop it, so I'm trying not to think about it and hopefully we will have everyone at pre-season."