Besic arrived from Ferencvaros in 2014 in a £4.8m deal but he believes he is still getting used to life in the Premier League.
He said: “When people look at my game, before and now, I think I have improved a lot in many different areas.
“But, like you have seen, I am still adapting to the league and I will continue to work hard and give my best.”
He is also targeting silverware with the Toffees as they look to end a 21-year wait for a trophy.
He added: “We always speak about things we want to achieve, Europe and other things. We have to show it on the pitch and do it. The next 12 games and also Chelsea in the FA Cup, I hope we can do our speaking on the pitch.”