The Toffees leapfrogged Tottenham into fourth courtesy of Sunday's last-gasp 2-1 win at Goodison Park.
The only time Everton qualified for the Champions League was in 2005 but they are well-placed to repeat that feat.
"It doesn't mean a lot to us now," said Distin. "It is obviously better to be there than in the bottom four but it is too early.
"The more time goes and more you stay in this position then the more you start to believe.
"But we have to get through the Christmas period and see where we are and then we can start dreaming.
"But I can't see any easy games. Every game is important and we are really focused on what we want to do."
Distin believes Everton are playing their best football since he joined from Portsmouth in 2009.
"We've played some really nice football, we are a lot more offensive than we used to be," he said.
"We can play long ball to Felli (Marouane Fellaini) or short down the sides with Leighton Baines or Kevin Mirallas.
"Even sometimes the physios come to watch training and after when we're having a massage they will say 'training was great today'.
"There is really great quality, a good atmosphere and great determination.
"I've been here four years and I think it is the best football squad we have and it is very attractive for the fans and they enjoy it."
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