David Moyes' men made an encouraging start to the season by winning their opening two Premier League matches, before their 100 per cent record was ended by West Bromwich Albion. But recent signing Mirallas, hoping to make his first top-flight start in Monday's home clash against Newcastle, says he has already seen enough to suggest his new team can challenge for a top-six place.
Everton have not played in continental competition since crashing out of the Europa League to Portuguese side Sporting Lisbon in February 2010. They narrowly missed out last season after finishing in seventh place, eight points adrift of sixth-placed Chelsea.
"We have a really good team and we've started well," said Belgium international Mirallas. "I hope that this season will be even better for the club than last year. The aim is to qualify for Europe, through the Europa League at least. "Last year we weren't too far away, and I think this year we'll get there."
Mirallas, who signed in a £6million deal from Greek club Olympiakos last month, has joined the growing legion of Belgians currently plying their trade in the Premier League.
"It's going to be enjoyable playing almost every weekend against a compatriot, someone from the national team," he added. "It already happened to me with Romelu (Lukaku, of West Bromwich Albion). We're very proud that there are a lot of Belgians playing in the best league.