Toure is counting on the Chilean to help bridge the gap on defending champions Manchester United.
"Last year, we have to be honest, United were much better than us," said the former Barcelona midfielder.
"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."