Negredo took his goal tally for the season to 18 with a brilliant hat-trick in City's 6-0 rout of West Ham in the first leg of their Capital One Cup semi-final on Wednesday.
The Spaniard, signed last summer from Sevilla for £20million, has also formed effective partnerships with first Sergio Aguero and now - in the injury-enforced absence of the Argentinian - Edin Dzeko.
He also showed against West Ham how hard-working he is all round the field, notably when he chased back to his own area - when City were leading 3-0 - to win a tackle.
Pellegrini said: "On more than one occasion he ran back to win the ball.
"He recovered balls, he scored three goals, he was the link with the midfielders - it was a complete game.
"I always thought he was the player this team needed. I knew him very well from the nine years I was in Spain, so when he arrived here I was absolutely sure he was the striker we needed."
Dzeko also struck twice against the Hammers at the Etihad Stadium and Pellegrini was pleased with how the pair combined.
The former Malaga coach said: "Both of them played very well - and also the midfielders (David) Silva, (Yaya) Toure and (Samir) Nasri did well.
"That's why when we made a squad at the beginning of the season, we brought in important players.
"You normally have a lot of injuries during the season, and Alvaro and Dzeko have replaced Aguero and (Stevan) Jovetic, who is another important player who can't play at the moment.
"It is important for the team that we don't depend on just one name."
Negredo believes he is probably enjoying the best spell of his career, although he still thinks he can improve.
The 28-year-old said: "My feelings and my game make me think this could be the best moment, we just have to wait (on that), but I'm feeling comfortable.
"I score a lot of goals and hopefully I can make some assists.
"Hopefully I can continue like this for the rest of my career.
"The only goal is to grow, to improve as a player and become better."
Negredo's value has undoubtedly increased during his short time with high-flying City.
Just 12 months ago he was being linked with a £13million switch to Everton but he feels he moved to England at the right time.
He said: "There were some rumours but I just wanted to finish the season with Seville.
"I wanted to wait until it got to the summer before I started looking at other options.
"I never really considered the possibility of moving in January."