The Goodison Park outfit have lost only one of their 10 Premier League matches this season and sit seventh in the table, just a point adrift of second-placed Chelsea.
They were held to a goalless home draw against Tottenham on Sunday, but Distin feels they have lots more improvement left in them.
Ahead of a tricky month that will see them play Liverpool, Manchester United and Arsenal, Distin told Everton's official website that he expects Martinez, who took over from David Moyes in the close-season, to help them have a strong season.
"All the players are different but it is nice to see - he (Martinez) is always very positive and honest as well," the Frenchman said.
"To be honest, it was the same with the previous manager. That is the mentality of the club, it has always been very positive.
"The fans have always been very demanding, the players as well. That is just how it is here.
"And even if we get results, we are still adapting to the new style of the manager, the new philosophy of playing. We have had good results but nobody feels, 'That's it, we understand everything'. We don't. We are still adapting.
"It takes a bit of time. It is very early, even if we had gone second it wouldn't change anything. It is a very long season but we are still up there. We are enjoying it."
Distin has played every minute of Everton's Premier League campaign this season.
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