Distin was speaking to the All Together Now podcast.
"It was a good relationship, but there was a bit of tension as well," the now 41-year-old said.
"I don't hold back, I say what I have to say. It was the same for them [the Everton fans] as well.
"So we came to blows a couple of times, but I think it was healthy. At the time I remember I started to use social media because I wanted to be closer to the fans, I wanted to say what I had to say without going through a newspaper or anything.
"That allowed the fans to contact me directly as well. That was tough, but winning or losing I was there.
"I was taking critics or whatever came to me. I did enjoy it, it helped me get to know fans a bit more.
"There are pros and cons but altogether it was a good experience, possibly that's what got me closer to the fans.
"My personality on the pitch I've never been the best player in the world, I've never assumed that. But what I can do is give 200% and I managed to do that every time.
"Sometimes it's enough, sometimes it's not."