Signed to much fanfare in a club-record deal, the 27-year-old has only impressed in fits and starts since swapping Rome for the south coast in the summer.
In recent weeks, though, there have been promising signs from Osvaldo, highlighted by last weekend's exquisite solo effort in the 1-1 draw with Manchester City.
It was the kind of goal that will not only strike fear into Saturday's opponents Newcastle, but also Roy Hodgson's side as Osvaldo is currently part of the Italy side included in England's so-called World Cup group of death.
"We believe that he still has a big margin to improve, he has a lot to go still," Saints boss Pochettino said.
"Right now, he is in the process of growing and adapting to this league.
"I think he needs to understand that the goal he scored puts him on the right path, but he stills has to learn, still has to improve.
"He still has to mature and still has to keep on working to be able to deliver that kind of goal every week.
"Right now he is part of the Italian side and could very well play for them.
"I think it is an advantage for the England manager and players to have him here, to see how he plays and learn a lot more from him."
Osvaldo is likely to keep his place in the starting line-up this weekend at St James' Park, where Saints could again be missing seven first-team players through injury.
Artur Boruc, Kelvin Davis, Nathaniel Clyne, Danny Fox, Victor Wanyama and Guly do Prado are all definitely out, while Morgan Schneiderlin may not travel due to a pelvis complaint.
"The only option that we are analysing that maybe be on the list for Saturday's game is Morgan Schneiderlin," Pochettino said.
"If he were to be on the list, he wouldn't be physically fit to play the full 90 minutes.
"Tomorrow we will make the final evaluation to see if he is able to play a few minutes on Saturday or if it is better that he stays here and keeps on training."
Those injuries have seen a number of teenagers fast-tracked into the first-team fold.
James Ward-Prowse, Luke Shaw, Calum Chambers and Harrison Reed all featured in the 1-1 draw with City, while Sam Gallagher was an unused substitutes.
The latter netted a hat-trick for Southampton Under-18s as they thrashed rivals Portsmouth 7-0 in the FA Youth Cup this week, but such displays will not see Pochettino rush such players' progression.
"I was at the game and there were many first-team players that were there as well watching the game," he said.
"I think we need to give him time and not just Sam Gallagher, but a large percentage of the players that played in that game. They could have their chance with the first-team.
"We need to be patient with them overall and understand that every single case involves an individual and that they all need their own individual time to progress, mature and be part of the team."
Pochettino's trust in the club's young players led to him recently saying such strength in depth meant he was not worried about having to do business in January.
Despite that, Werder Bremen's Aaron Hunt, Valencia attacking midfielder Sofiane Feghouli and Wolfsburg's Diego, a player he managed at Espanyol, have all been linked with a move to St Mary's.
Asked if he was interested in such moves in January, Pochettino said: "No, not right now.
"So far we haven't actually analysed or look at any one player. None of those players are of interest."