Tuesday's 3-1 defeat at Emirates Stadium means Arsenal will end the season without silverware for the fourth successive campaign.
Adebayor admits the trophy drought has been too long and insists the club must do everything they can next season to secure some success.
"It has been a long time [without a trophy] but I joined in 2006 and I feel sorry for not winning anything in three years," Adebayor told Sky Sports News.
"Now for next season I don't know how we are going to do to be honest. I don't know how we are going to manage.
"What we are going to try to do is score with our head, our toes, whatever. We just have to try and bring trophies to this club."