"I will do everything that it will take to come back next season and show how good I am - show character, show more personality, show desire for this club," Adebayor declared.
"I have been doing my best, giving 100 per cent in every single game.
"Do not forget last season I played without injury and this time I got three injuries. That makes it quite difficult."
Adebayor maintains all is not lost for Wenger's young squad, which next season will have January signing Andrey Arshavin eligible for the Champions League.
"We are learning things and just want to achieve," he said. "We just have to believe and keep going.
"We are very disappointed for the fans for the way they believed we can do it.
"We are very sorry for that and it is very important for the next season that we are here to play and bring glory to this club.
"As soon as we have the chance to win the first trophy, many will follow."
Adebayor said: "This season was a little bit difficult for everyone, so now we just have to play for our dignity, show character and hopefully come back."