The Montenegro international, who joined City in a £22m deal from Fiorentina in the summer, has been limited to three Premier League appearances this season due to hamstring and calf problems.
He is in the squad for the Capital One Cup semi-final second leg against West Ham United on Tuesday and Pellegrini backs the versatile forward to make an impact before the end of the campaign.
"He came here with the illusion of playing in the Premier League," he told reporters. "He was a very important player in Italy for Fiorentina and I still believe he will be a very important player for us.
"He can really start playing often in the next three months and I think he can be the player we hoped he would be. It's very difficult to be happy when you're not playing and you have so many injuries but he's conscious that he will be 100 per cent fit and demonstrate why he's here.
Pellegrini added: "Stevan can play as a forward or a midfielder - it's a position he played sometimes at Fiorentina. We'll see when he's fit if he can do it."
Jovetic scored twice in the 5-0 thrashing of Wigan Athletic in the League Cup third round in September - his only City goals to date.
Pellegrini's side lead West Ham 6-0 heading into Tuesday's match.