The Netherlands international, who made a £24m switch to Merseyside during the summer, was part of the Ajax side that fell to a 2-0 defeat to Manchester United in the Stockholm final four months ago.
Klaassen admits that he is still not fully over that loss, but it is not something that he has discussed with ex-Man United skipper Wayne Rooney since both men arrived at Goodison Park.
"I don't want to talk about the final with Wayne at all. I still feel the pain. It was not good," The Mirror quotes him as saying. "True I came so close to winning it last season, but I don't need to lose in a final to be hungry for this campaign.
"We want to reach as far as possible. We all start at zero. We have to start with a win, get confidence and space. Our last result [against Tottenham] was not good, but we try to pick it up. Playing in Europe helps every player. We face different cultures of playing in.
"The results have not been good but I like the life and the club and my teammates. I am enjoying it. I need to improve, everyone needs to improve and we will be there."
Everton get their Europa League group-stage campaign up and running on Thursday night with a trip to face Serie A side Atalanta BC.