The Toffees came back from 2-0 down to beat West Bromwich Albion on Monday night, and Kone saw plenty to be encouraged by in the contest.
The Ivorian says that the Toffees showed their class at the Hawthorns, and he believes that an exciting season could lie ahead for his side.
“I think it was a really great performance for the team and a great victory,” Kone said. “If we can play like that then I think this year Everton will be able to do something in this league.”
Kone scored in the game against West Brom, with Romelu Lukaku grabbing the other two goals which provided Everton with victory.
It was an example of the attacking class that the Merseyside outfit have at the club, as not many teams will score three times against West Brom this season.
The Baggies are one of the most organised sides in the Premier League, with Tony Pulis famed for his ability to tighten teams up defensively.
Everton are currently in fifth place in the Premier League table, and could climb into the Champions League spots if they are able to beat derby Liverpool at the weekend in what promises to be a keenly-contested Merseyside derby.