The blue half of Merseyside have won four and drawn one of their opening Premier League games to give them a second-place spot in the table.
"Before I signed, I was looking at the Europa League being a more realistic ambition," Mirallas told the Liverpool Daily Post. "But certainly now as the season has got underway, we have got a good crop of players here and are playing some really nice football.
"It's fantastic that we are second and our ambition now has to be to stay up there and put pressure on those around us. It's a long season though and there's a long way to go, so we'll have to see what happens."
Everton travel to the DW Stadium to take on Wigan Athletic this weekend.