The Gunners' hopes of reaching the final in Rome were effectively ended after just 11 minutes at Emirates Stadium, where the holders raced into a 3-0 aggregate lead with two early goals.
Toure said: "Nobody was expecting a lot for us this season and we showed great spirit and we are really proud of what we have done.
Manager Arsene Wenger admitted it was one the most disappointing nights of his time in charge of the Gunners, whose last trophy came back in 2005 with the FA Cup.
Arsenal have secured fourth place in the Barclays Premier League following an unbeaten run of 21 matches, but another campaign which promised so much has failed to deliver. However, Toure is in no doubt the young squad will have learnt some important lessons after being exposed by the talent of Cristiano Ronaldo and England forward Wayne Rooney.
"We are not far behind those teams. We want to win and we will try to come back and be strong," declared the Ivory Coast defender.
"The only thing we can do at the minute is to just keep players, and if we can bring some more that would be fantastic.
"The spirit is good and we hope we are going to stick together and fight together again next season."
Toure is now fully focused on his future at Arsenal, having handed in a transfer request during January after a reported training ground bust-up with William Gallas.
"When you win trophies it becomes like a habit for you," he said. "This time we did not win anything, but when we get the first trophy, you will see more from Arsenal."