Manuel Pellegrini's side have already picked up the League Cup this season, but crashed out of the FA Cup and the UEFA Champions League in the space of four days.
After defeats to second-tier side Wigan Athletic and Spanish champions Barcelona, City have just the Premier League title race to focus on.
City are nine points behind leaders Chelsea with three games in hand and face a stiff challenge to overhaul Jose Mourinho's in-form side.
Yet Toure has bristled at the suggestion that his club's campaign would be deemed a failure should the League Cup represent their only trophy.
"A failure? Why? Why would it be a failure? We have already won a cup, so you can’t say that," he said.
"Football is a competition and only one team can win each of them. So don't say we would be failures because we have won something already, but now we want to win more.
"Teams come and they are desperate to beat us, though, so it is always tough. Teams are very motivated against us and you have to understand we are not a machine.
"We just need to work, keeping working and try to win all of the games. We know it’s going to be difficult, but when you lose games, you learn more about yourselves. Sometimes when you lose it’s not bad and we learnt by playing against a big team like Barcelona."
In what was City's first venture into the knockout stages of Europe's premier club competition, they were beaten 4-1 on aggregate by Barca thanks to goals from Dani Alves and Lionel Messi in either leg.
Toure feels signs of improvement were shown in the defeat to his former club and backed City to be stronger for the experience.
"They deserve to go through. Over the two games they were better, but they have more experience at this level than us," he added.
"We are out but we have to focus on the Premier League and then see what we can do in this again next time.
"We've shown that we have improved. We have to move on and think about the Premier League. With the players we have I still think we can do it."
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