The 2012 Premier League champions are determined to get their hands back on the crown, and are well-placed to launch an assault on top honours.
A 3-2 win at the Liberty Stadium on New Year's Day took them briefly to the summit, until Arsenal saw off Cardiff City later in the day and reclaimed their lofty perch.
City are, however, moving ominously through the gears and have started to get their form right on the road - an issue which was threatening to hold them back.
Toure says landing major silverware is now the only target for those in the City camp, and domestic honours are considered to be a top priority.
The Ivorian midfielder told Sky Sports on the importance of seeing off Swansea: "It's very important because we continued to fight until the end.
"For the team and the club, we want to win this trophy. I think if we continue like that, at the end of the season we will be happy.
"In the first half today, the team worked very well. We had to manage playing against a good side and Swansea created a lot of problems.
"I think we did a fantastic job against a good team. I think we deserved the win today."
Toure was among the goals again in South Wales, taking his Premier League tally for the season into double figures.
On a personal best return which has been secured with half of the campaign still to come, he added: "It's amazing. I'm working hard and trying to help my team-mates.
"Today I was a bit lucky, but we have three points and it's fantastic."