"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," the Togolese striker told the club's website.
"But next season we have to come out like a killer to do something. We have the quality. We know that because we always seem to score first," added Adebayor.
Despite being in the lead twice last week, the Gunners lost to Liverpool in the Champions League and Manchester United in the Premier League to get ousted from both competitions.
Meanwhile, Captain William Gallas blamed his side's poor luck for their trophy-less season.
"You can play well, but if the luck is not there, then you will win nothing. The luck went from us a few months ago. People have to understand that," Gallas told Arsenal.tv.