The Toffees' 3-2 win over Swansea City on Saturday has moved them within eight points of fourth-placed Arsenal, with a game in hand and Arsene Wenger's men still to come to Goodison Park.
Although the Europa League is a more likely outcome, Distin has said that Everton will push for fourth place in the Premier League until it is mathematically impossible.
"The dream is always alive as long as it is mathematically possible," the Frenchman told PA. "We are not in a position where we have to focus on the team above us. We cannot depend on them (dropping points) so there is no point looking at it now.
"Every single game is important. This one is no more important than the previous one. We just want to win games.
"You have to win. If you want to be successful, you can't start a game thinking it will be okay to draw this one."
Everton currently sit in fifth place on 54 points.