And the Frenchman admits if, as a player, you do not grasp it within a couple of weeks of arriving manager David Moyes is quick to point it out to you.
The players' never-day-die attitude was exemplified in their last-gasp 2-1 win over Tottenham on Sunday when Steven Pienaar and Nikica Jelavic scored within 88 seconds of each other to secure a deserved three points after Clint Dempsey's deflected opener against the run of play.
"We always believe we can win and we proved it again," said the centre-back, who stressed they were not happy to settle for a draw after Pienaar's 90th-minute equaliser.
"We were unfortunate with the goal we conceded but we never stopped believing and we always kept fighting.
"We don't have to think about it, that is the mentality at Everton and after two weeks at the club that is how you behave because you follow the rest of the squad.
"Whether we are 1-0 down or 2-0 up, we play from the first second to the last second.
"Personally I've always been like that but if you are a player who is not too much like that you change your attitude pretty quickly and you follow everyone going in the same direction.
"When you join a club like Everton it feels like home after two weeks and it comes naturally - if not you have the gaffer on your back at the end of the game and you don't want that."
The win was only the second in 10 matches but it restored Everton's place in the top four.
Distin insists their current position is not something the squad currently think about but their Champions League dreams may start to materialise if they still occupy a top-four slot in a month's time.
"It doesn't mean a lot to us now," he added.
"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."
Nevertheless, Everton are better equipped than they have been for a long time to challenge for a top-four place.
The last - and only - time they qualified for the Champions League was in 2005.
That was four years before Distin arrived at Goodison Park but the defender believes Everton's football is the best he has seen since he joined from Portsmouth.
"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.
"It has been frustrating for them with the draws we've had but they have to remember those were the kind of games we would have lost last season.
"They have to keep believing because we believe."
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