Everton beat the Gunners 3-0 on Sunday to move to within a point of fourth place, currently occupied by Arsene Wenger's side, with Roberto Martinez's men also holding a game in hand.
Mirallas believes Arsenal are suffering from the weight of expectation, but claims beating the north London club will give Everton added confidence heading into the Premier League run-in.
"There's so much pressure on Arsenal now because things are in our hands," he told the Liverpool Echo. "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.
"It was a fantastic performance. It was a must-win fixture for us and we knew it was vital we scored first.
"We know having won that, with our game in hand we can grab fourth place ourselves."
Everton were beaten 4-1 by Arsenal in March when the sides met in the FA Cup and Mirallas admits the pain of an Emirates elimination inspired them on Sunday.
"We sat and had a good deep think in the dressing room at the Emirates after the quarter-final," he added.
"Then we said we have to put that behind us and concentrate on the league. We looked at it and said there were 10 games and enough points for us to really fight for fourth.
"We were determined to get some kind of revenge because we conceded four goals down there and it hurt. This was excellent revenge. We're in the right place."
Champions League dream
Belgium forward Mirallas experienced Europe's premier competition during spells at Olympiakos and Lille and holds hope of a return to continental competition.
"It would be great to make the Champions League; for everyone here," he said.
"Each and every one of us. But we need to keep going and hope it can happen.
"I have played in that competition at two of my previous clubs and when I signed for Everton that was my ambition to achieve it again in my career.
"That's what I'm dreaming of now."
Speaking to Sporting Telenet, Mirallas also revealed his desire for striker Romelu Lukaku to stay at Goodison Park, claiming it would be essential for European success.
"I hope that we qualify for Champions League and that Romelu Lukaku will be still playing for us," he said. "We need him and he feels well over here. Why would he go elsewhere?"