In what has been a fine start to their Barclays Premier League campaign, the Toffees claimed another creditable point as Spurs' visit to Goodison Park ended in a stalemate.
The result left the Merseysiders seventh in the table but a victory could have lifted them to second and further underlined the positive start to the Roberto Martinez era.
Distin said: "Right now we are in a spirit where we want to win every single game.
"When we draw at home against Spurs and feel disappointment, that shows where the team wants to go. It is great.
"We feel like it is two points missed but I think it is a fair result.
"In the first half I think they dominated us and in the second half we were much better."
Distin's assessment is a reasonable one. Spurs controlled possession and created the better chances before the break as Everton struggled to gain and retain the ball.
The hosts commanded more control in the second half and Hugo Lloris - who controversially played on after a nasty collision with Everton's Romelu Lukaku late on - was the busier goalkeeper.
Distin said: "You have to learn from your mistakes and adapt your position.
"They had a gameplan and we had to change our gameplan, and that worked fine.
"It was still a good game. We had some great chances and didn't concede a goal. At home, that is good."
Martinez's enthusiasm for his task at Everton is obvious and Distin feels that has added to the strong culture already put in place by his predecessor David Moyes.
The veteran Frenchman, 35, said: "All players are different but it is nice to see - he is always very positive and honest as well.
"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.
"It is great. 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."
Sandro, Roberto Soldado, Andros Townsend and Lewis Holtby all had early chances for Spurs before Everton began to get into the game.
They eventually responded through Leon Osman and other chances fell to Kevin Mirallas, Steven Pienaar and Lukaku.
Both sides had penalty claims after incidents involving Jan Vertonghen and Seamus Coleman in each other's area, but neither were given.
Lloris, who argued for the right to play on after briefly being knocked out in the Lukaku clash, made a telling late contribution by saving well from Gerard Deulofeu.
Distin believes Everton now just need to continue in the same vein.
He said: " Everything is good so far.
"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, formerly of Manchester City and Portsmouth, is also losing none of his enthusiasm for the game and is feeling in as good form as ever.
He said: "I enjoy playing, at my age you have to enjoy it.
"I'm feeling good - physically I feel good. Everything is fine.
"Game after game I don't ask myself too many questions and so far so good. It's perfect."
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- Barclays Premier League