The midfielder believes the confidence of winning the first piece of silverware of the season could boost the Blues' push for other trophies this term
Manuel Pellegrini's side is still battling on four fronts, but Toure believes the Blues can only start thinking about creating history once the club has picked up some silverware against the Black Cats at Wembley.
The Ivorian moved to Eastlands from Barcelona in 2010 having won the Champions League, Copa del Rey and Primera Division in 2008-09, but he says it is difficult to do the same in England.
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"We want to take the season game by game and we need to be ready for the final. It is very important for the club and for the fans. After you win the first you have the confidence to continue and have your mind focused on winning games. We want to finish with the game on Sunday then move forward."
Yaya was part of the City side that was surprisingly beaten by Wigan Athletic in the 2013 FA Cup final at Wembley, and the Ivory Coast midfielder believes the team have learned from that disappointment and will be sure not to allow it to happen again.
"For me personally, every game has a different story. We have missed a couple of games, like the final against Wigan in the FA Cup, but we just need to be ready for Sunday," he added.
"We don’t want to feel like that again and hopefully this time we will win this competition."
Pellegrini, who is chasing his first trophy as a manager in England, has been boosted by a return to fitness for top scorer Sergio Aguero and Yaya is thrilled to see the 25-year-old back in contention ahead of such a crucial encounter.
"It’s very important because we need our best players. We have missed him for a couple of months, but now that all our players are fit and wanting to play it’s great news," he said. "I hope Sunday we’re not going to miss him because finals are always controversial and one mistake can be the difference. Hopefully he will be fine."