The former Malaga coach got his first victory as City boss in a 1-0 win over South China in Hong Kong on Wednesday, having only arrived in the region a day earlier after the death of his mother.
Toure said he hopes the Chilean, who replaced the sacked Roberto Mancini, can bring trophies to the Etihad after rivals Manchester United romped to the Premier League title last season.
"Last year, we have to be honest, United were much better than us," said the former Barcelona man, 30.
"We are working and trying to understand and learn from the new manager, who had a fantastic record in the past in Spain."
He added of Pellegrini: "Unbelievable, great things, his ability to manage is unbelievable and he's doing fantastically well. We are all focused on him and trying to understand what he wants us to deliver and what he wants us to do on the pitch.
"He's an unbelievable guy, a very good guy, and dedicated to his work, and you can see his commitment. He's a very good choice for Man City and I hope he's going to bring a lot of trophies to Man City.
"When you change mangers, sometimes it is quite hard because you need to adapt to the new formation. But with the new signings I think it is going to be very exciting."
City have been the biggest spenders over the summer as they attempt to wrestle the Premier League crown back from Old Trafford, shelving out 83 million pounds ($126 million, 96 million euros) on new players.
They have brought in strikers Alvaro Negredo from Sevilla and Stevan Jovetic from Fiorentina, as well as Spanish midfielder Jesus Navas and Brazil midfielder Fernandinho from Shakhtar Donetsk.
"They are amazing, amazing. I already know them because some of them have come from Spain... They are great players and we welcome them to Man City.
"I hope the fans will enjoy them and they will help the club lift a couple of trophies this year."