The guitarist reveals the core four-piece of himself, Joe Strummer, Paul Simonon and Topper Headon came close to getting back together on a couple of occasions - but it was never the right time.
Jones, who recently toured with Simonon as part of Damon Albarn's Gorillaz, tells Rolling Stone magazine, "We were just all fed up with each other. The bigger it got, the more difficult it became. We battled through constant issues.
"When you're together all the time you're going to get fed up with people, especially without breaks. And then we started to get into whatever we were into individually, and that became an issue. I don't think the music was ever affected, or the stage show. It was all going on behind the scenes. We could have dealt with it better, in hindsight."
Jones appeared onstage with Strummer just before the singer died in December, 2002, and admits that at the time there was talk of a get together at their induction into the Rock & Roll Hall of Fame.
He adds, "There were a few moments at the time... I was up for it (Hall of Fame reunion in 2003), Joe was up for it. Paul wasn't. And neither, probably, was Topper, who didn't wind up even coming in the end... It didn't look like a performance was going to happen anyway. I mean, you usually play at that ceremony when you get in. Joe had passed by that point, so we didn't.
"We were never in agreement. That's why we never got back together in the first place. It was never at a point where all of us wanted to do it at the same time. Most importantly for us, we became friends again after the group broke up, and continued that way for the rest of the time. That was more important to us than the band."