The Toffees are currently taking part in the Guiness International Champions Cup in the United States and it has given their French defender a taste for future European campaigns
The pre-season tournament in America has seen the Toffees face both Serie A champions Juventus and Spanish giants Real Madrid, with Roberto Martinez's men beating the former on penalties before losing 2-1 to Madrid.
Despite failing to make it to the final, Distin feels that the tournament has given his side a valuable taste of playing against top European opposition, as they aim to push for the Champions League places in 2013-14.
"We don’t need to be reminded how good European football is. Every player wants to play in Europe," he told the Liverpool Echo.
"It’s amazing and when you see the last two games they’ve been fantastic. Even if it’s pre-season – it just whets your appetite.
"That was like a Champions League game. You can’t find better competition than the two teams we’ve played so far. Unless you play against Spain or Brazil I don’t think you can get better than that.
"I even got the chance to shake hands with Zidane [Real assistant coach]. I had to wait nearly 36 years to do that!"
The Frenchman will likely have to wait a little longer for that opportunity to come again though, with Everton having failed to qualify for the Europa League for the third consecutive season.
Martinez's men will take on Valencia in the International Champions Cup on Wednesday before finishing their build-up with a clash against Real Betis on Sunday.
They open the Premier League season against Norwich on August 17.