Jesus Navas found the net after just 14 seconds at the Etihad Stadium and went on to complete the scoring in the 90th minute, after a Sergio Aguero double.
Alvaro Negredo also struck in the second half, while Sandro scored an own goal as City sent out a message to their title rivals with a performance that Toure attributes to Pellegrini's rousing speech, which ordered them to respond to their surprising loss to struggling Sunderland before the international break.
"The manager's speech before the game was unbelievable," Toure told reporters.
"It is always difficult when you lose a game like we did at Sunderland. It is hard for the players.
"Football is so strange. But we have come together as a team because we want to regain the Premier League."
City have scored 26 goals in their seven home Premier League matches this season and currently sit fourth in the table, having picked up only four points from a possible 18 on the road.