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Jovetic, 24, endured a frustrating debut campaign at City, with injury and illness restricting him to only 11 league appearances, but he appears rejuvenated after a successful pre-season.
He scored either side of half time in Monday's game at the Etihad Stadium and Pellegrini said it was reward for his determination.
"He was very unlucky last season, but we never had any doubt about his quality," Pellegrini told reporters.
"I'm very happy for him, because after such an unlucky season, he deserves to start this season the way he's playing."
Jovetic said: "There are so many beautiful moments now after so many problems last year, but I don't want to think about that as it's the past.
"I just want to enjoy [playing] with this team, with these players, and to win as many titles as we can."
With Alvaro Negredo sidelined by injury and Sergio Aguero working his way back to full fitness after his exertions with Argentina at the World Cup, Jovetic has acquired extra importance for the defending champions.
But Aguero also made an impact against Liverpool, scoring just 23 seconds after coming on for Edin Dzeko in the second half.
Pellegrini said that Dzeko would undergo tests after the Bosnian striker took a kick to the leg, but described it as nothing important.
Jovetic's display took the spotlight away from Mario Balotelli, the former City striker, who watched the game from the director's box after completing his £16-million (R283.7-million) move to Liverpool from AC Milan.
The Italy international arrives with a reputation for causing trouble, but Liverpool manager Brendan Rodgers described his transfer as a calculated risk.
"I think that in the market to get someone in at that quality, the deal for us was very good," said Rodgers.
"He is a world-class talent and it is an area we need to strengthen." - AFP