The England international paid tribute to the Chilean's winning mentality while the Frenchman believes his manager's calmness has played a key role in their success
Nasri and Vincent Kompany scored the goals as City saw off the Hammers 2-0 at the Etihad Stadium to finish top by two points from Liverpool, who beat Newcastle 2-1 at Anfield.
The triumph sees Pellegrini secure his second trophy inside 12 months in England since replacing Roberto Mancini last summer, and Nasri and Hart believe the Chilean has spurred City on to greater heights.
"Manuel Pellegrini is a winner," Hart told Sky Sports. "He believes in what he does."
Nasri added: "I'm so happy for the manager too because it's his first title in England.
"He remained calm all season for us to play attractive football and it was a pleasure to work with him. The Liverpool game against Chelsea, I think that was the twist of the season.
"It’s an amazing feeling. We’ve really been friends this year, everyone put their ego to the side."
Hart also believes City's title win sets him up perfectly to head into this summer's World Cup in Brazil full of confidence.
"It was calmer than the other season, but it was a very tough season," he continued.
"It's claimed this was the best Premier League ever. Every team has played a part this season. It couldn't have set things up for the summer any better."