And he is already thinking about his own plans at the Barclays Premier League club for next season.
Bought from Roma in the summer for some £15million, Italian forward Osvaldo managed just three goals in 13 appearances and following a training-ground bust-up with defender Jose Fonte was shipped out to Juventus on loan, with a view to a permanent move.
Pochettino feels the way the team responded in recent weeks - which also followed the high-profile departure of chairman Nicola Cortese - with an unbeaten run of seven games in all competitions, shows their true character.
"This team has always had a very strong mentality and any departure from this club is going to affect people in a personal manner, but professionally the team puts in very good performances, takes on a lot of responsibility and puts in a lot of effort," Pochettino said.
"The work rate is always amazing with these players and with all of these players, this club has a great future."
Argentinian Pochettino has himself been linked with a move away from St Mary's Stadium, but indicated he was in it for the long haul with he Saints.
He said: "I dont really listen to these kind of rumours.
"They flatter the club and flatter the players that make up this club.
"Nearly all of our players have been linked with other clubs, which flatters the philosophy which is in place at this club."
Pochettino added: "On a personal matter, I am very calm on my future and am already thinking ahead on planning ahead for next season."
Southampton now face three away games, starting at Hull on Tuesday night, with an FA Cup fifth-round tie at Sunderland before the trip to West Ham on February 22.
Pochettino is expecting his side to maintain their positive approach.
"We have been on a very good run, been having very good performances and getting very good results and we just need to carry on in the same manner that we have been playing, so our focus is to play the same way tomorrow at Hull," said Pochettino, whose side drew 2-2 with Stoke on Saturday.
"We always prefer to play at home but the team has shown the right consistency and mentality to play away from home as well."
Hull moved themselves away from the relegation zone with a 2-0 win at Sunderland and Pochettino is relishing the prospect of tackling Steve Bruce's well-organised team.
"Hull is a very aggressive side, a very tough side to play against and frankly a side that I like how they play." he said.
"We have full respect for Hull and for sure it is going to be a very tough game against them."
Midfielder Victor Wanyama is pushing for a recall after recovering from a hairline fracture in his leg.
Striker Sam Gallagher, meanwhile, could be in the travelling party as the 18-year-old has returned to training from compassionate leave following the death of his father.