Toure, who was part of the Gunners' 'Invincibles' side in 2003-04, played 90 minutes in Paris two years after that title win as Arsene Wenger's side let a one-goal lead slip in the final 14 minutes to lose 2-1 to Barcelona.
Ahead of Liverpool's Europa League clash with Augsburg, the 34-year-old revealed that he is desperate for the club to succeed in Europe, as well as to win a first trophy in his time at Anfield later this month.
He told the club's website: "I’ve played in a Champions League final and haven’t won it and I still think about that every day. I’m a winner and everywhere I go I want to win and do my best to win.
"I thank God for this chance and I really, really want to win a trophy for this club because it’s such a great club. I can see that to win a trophy here would be amazing and I want to be part of that.
"When you play for Liverpool you’re expected to be one of the teams that can win [trophies] but you have to show that on the pitch. That’s what we will try to do."
The Ivorian will have a chance to win a first trophy in his time with the Reds, and a first League Cup triumph of his career, when Jurgen Klopp's side take on Manchester City in the Capital One Cup final at Wembley on 28 February.
Before that, however, the Reds have both legs of the Europa League last 32 tie against Augsburg on the horizon, with the first match taking place in Germany later on Thursday.