The Black Cats were minutes away from a crucial victory over Manuel Pellegrini's side, but were denied the three points as keeper Vito Mannone spilled Samir Nasri's shot into the net.
Poyet told the club's official website: "We were doing things right but couldn't get anything out of the games, then we went to Man City and did something very special.
"We have to go there with the same mentality. Yes, they have quality, but let's not worry about them and just play our game.
"It's a tough task but what a nice one if you do it, because you will make history and become the first team in the Barclays Premier League to beat Chelsea and [Jose] Mourinho at home."
Sunderland are 20th in the Premier League, six points adrift of safety with five games left this season.