The Toffees have faced former Champions League winners Juventus and Real Madrid in their past two pre-season friendlies in the USA.
"We don't need to be reminded how good European football is. Every player wants to play in Europe," Distin 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 [Zinedine] Zidane. I had to wait nearly 36 years to do that!"
Everton start their Premier League campaign away to Norwich City on August 17.