David Moyes' side beat QPR 2-0 on Saturday to move to within three points of Chelsea, who currently occupy the final Champions League qualification position.
They travel to third-placed Arsenal on Tuesday knowing victory would close the gap on the Gunners to just a point.
Everton have never won at Emirates Stadium, though, and are without a victory away at Arsenal since 1996, but Mirallas believes the current squad are primed to end their North London hoodoo.
"There's always a first time for everything. Let's hope it's Tuesday," he told the Liverpool Echo.
"Everton could do well in the Champions League but there are some big games between now and the end of the season which we have to win in order to get there.
"You don't really know how you'd do until you were in it and the competition started, but it's a fantastic competition and I think we're ready for it.
"I've played at the Emirates for Olympiacos and I hope we can get the three points we need down there tomorrow.
"It will be vital in order to get European qualification and make it a beautiful end to the season."
Mirallas appears to be finding his best form again after a niggling hamstring injury scuppered the middle part of the season and threatened at one stage to end his campaign completely.
The 25-year-old is happy with his recent displays but is hopeful of a full pre-season in the summer in order to ensure an injury-free campaign next year.
He added: "In spite of my injuries I am pleased I've been able to achieve one or two good things this season on the field.
"But certainly with the proper preparation and an injury free pre-season, which I didn't get this season, it would really help and augur well for the following season.
"I think you can see I am feeling a lot better in myself when you see me play. Feeling physically fit helps a lot. Getting games under your belt and playing regularly helps your confidence as well.
"When you do feel strong and avoid injuries that helps your game."