The drummer was "caught stealing" from the group and was promptly axed by the other members. He joined My Chemical Romance in 2010, and has since been replaced by Jarrod Alexander.
Pedicone explained to Kerrang that he had reached his "wits' end" in the days leading up to the incident.
"Almost as soon as I began touring with MCR I ran into problems with a member of the band's crew who I'll not name. The problems were many, big and small, but some of them were large enough that they began to greatly impact me and, by extension, my family," he said.
"I'd reached my wits' end, and I made what was certainly the poorest decision of my life. I would have liked an opportunity to share my side of the story with MCR, an opportunity to express my remorse. I was never given one."
Pedicone added: "Rather than address the issues that I had with the crew member in an open and honest manner, I tried to make them look irresponsible. My intention was to make this person look incompetent. I had no intention of profiting whatsoever. Again, I cannot overstate how poor my judgment was in this situation; it was a tremendous mistake, and it's one I'll regret for years to come.
"I'd like to thank MCR's members, crew and supporters for giving me some of the best musical experiences of my life in the past several months. However brief our partnership, it was an honour and a dream come true to play with such a talented bunch of individuals."
> My Chemical Romance 'to record new album in autumn'
Watch the video for My Chemical Romance's 'Sing' below: