"Arsene is a great man and a great manager," said Adebayor, who has 20 Premier League goals this season.
"He has a vision to bring a lot of good players to this club like Alex Hleb, Kolo Toure, Emmanuel Eboue, Cesc Fabregas and William Gallas. They are his players. So, for sure, we will win something, no doubt about that."
Adebayor, 24, added: "We will never give up. Last season we finished fourth so we have made a lot of progress and we deserved something.
"I still believe we are still one of the best teams in the world. We know how to achieve things and we know how to play football.
"But next season we have to come out like a killer to do something. We have the quality."