The Merseyside outfit secured a 3-0 win over the Gunners to move to within one point of fourth with a game in hand.
The Gunners, who are now 10 points adrift of leaders Liverpool, have five games remaining to secure a place in next season's European tournament.
"There's so much pressure on Arsenal now because things are in our hands," the Liverpool Echo quotes Mirallas as saying. "They are almost obliged to be in the Champions League, that's what they do.
"They've qualified for years, but we are breathing down their necks and we can go fourth if we win our game in hand."
The Toffees are away to Sunderland, while Arsenal will take on West Ham United at the Emirates in their next league matches.