Kone was limited to 81 Premier League minutes across five substitute appearances last term.
In what proved his final outing of the season, against Hull City in October, Kone struck the woodwork before suffering a recurrence of a knee injury, which subsequently required surgery.
The 30-year-old is now keen to bounce back and show why he was signed from Wigan Athletic by Roberto Martinez.
"I was working hard at the time when I hit the post against Hull and it was really frustrating at that moment to get injured, because I realised the fans were still waiting - and the manager and his staff - to see the best of me in an Everton shirt," Kone told Everton's official website.
"I felt around that time I was getting into shape and getting into a bit of form on the training pitch. For me, it's now about working hard and making sure I come back at my top level of form so fans can actually see something of the real Arouna Kone, the best Arouna Kone."
Kone is well aware he has plenty to prove at Goodison Park.
"It's going to mean an awful lot to me to wear that shirt next season because I've not yet written any history, I've not made my mark on Everton or created my own chapter of the story that is this club," the former Sevilla and Levante man said.
"The season ahead, for me, is one where I have to prove my worth as a player and I accept that challenge and I'm ready to take that challenge on."
