The Black Cats head for the Etihad Stadium on Wednesday evening having slipped back to the fringes of the fight for Barclays Premier League survival following Saturday's 2-0 home defeat by Hull.
Poyet had previously dragged the club into 14th place, as well as a Wembley final, after a vastly-improved run of results, but with their next three league fixtures scheduled to take them to City, Arsenal and Liverpool, their plight could deepen significantly over the next few weeks.
However, they have won three and drawn one of their last Premier League games away from the Stadium of Light and remarkably, have beaten City on Wearside in each of their last four meetings and for those reasons, the Uruguayan insists they cannot be written off.
He said: "Every time we look at a home fixture, we think we are going to win and we haven't beaten anyone.
"I just try to take them as they come. The idea is to go there and try to get something from this game and something from the Arsenal game and then if we have to go to Liverpool, depending on the cup, the same.
"I don't think we need to analyse too much or give up before we play. We are going to play our game and we will see. You never know.
"We are not a team that you can say you know what is going to happen. We are a quite unexpected team, so we will see."
Poyet knows only too well the weapons opposite number Manuel Pellegrini has at his disposal even without the injured Sergio Aguero, Fernandinho and Samir Nasri.
However, he has no intention of trying to defend for 90 minutes and hoping for the best against a side which has uncharacteristically failed to score in either of its last two games.
Poyet said: "When I am a fan, I like to see the best players playing. When it's against you, of course not.
"It's not the same - Aguero is one of the best in the world, Fernandinho has been great and Nasri when he starts getting between the lines is a difficult player to play against, so there are plenty of things that mean in this game, maybe we can be lucky.
"That's without talking about the rest of the players they have and what they can do, but it's true that it could be a little bit different because they are not there.
"But I am not just saying it for the sake of saying it - we are going to play to win the game. Then if the opposition is better than you and they batter you and you get a point, you take it and run and go home.
"But the idea is to go and try to perform and see if we can play against them and be a difficult team to play against."
The sides will meet once again on March 2 with the season's first domestic trophy at stake, but Poyet, who will be without suspended defender Wes Brown on Wednesday night following his dismissal at the weekend, does not believe either manager will be able to take too many pointers.
He said: "I don't think so because those players we talked about before are going to be there for the final, for sure.
"But it's true that mentally for the players, it would be good if can get a good result.
"For some reason, it's away from home that we have been doing well, so now it's a big opportunity against one of the top teams."