The Toffees moved to within eight points of the fabled positions with a weekend win over Swansea, but are firmly seen as outsiders.
Everton have been in the battle for much of the season, but a slight dip in form over the winter period saw them slide away from the upper echelons of the division after an excellent start to the campaign.
Although the Europa League now looks to be the more realistic option for the Merseyside club, Distin says that while there is hope Everton will continue to fight:
“The dream is always alive as long as it is mathematically possible.” He is quoted by The Mirror.
“We are not in a position where we have to focus on the team above us. We cannot depend on them so there is no point looking at it now.
“Every single game is important. 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.”
Distin has already expressed worry at the prospect of qualifying for the Europa League, for which they are in competition with Manchester United and Tottenham for.