The Togolese frontman, who joined Arsenal in January 2006 from Monaco, is yet to win his first trophy with Arsene Wenger's team.
The London-based side are already out of the Premier League title race, but they're still holding out hope of winning the UEFA Champions League and FA Cup.
"As a player, you always dream of winning things," said Adebayor. "When I joined this club, I was told by most of my friends and team-mates that I had a great chance of winning something.
"But for the last three years I have gone on holiday having not won a trophy and with an empty heart. Now it's the time to achieve things.
"Maybe I want it more than the others, I don't know. We all have a desire to achieve things and that's the most important thing.
"There are always players who are more happy than others when you win things, that's normal, but the desire is there for everyone."