Peter Moores was recalled for a second spell in charge after Andy Flower stood down following England's 5-0 Ashes thrashing in Australia.
Former England spinner Giles appeared to be in pole position to replace Flower, having been the national limited overs coach since November 2012 and a member of the selection panel.
However, his cause was not helped by a poor run of results in one-day games in Australia and England's humiliating loss to the Netherlands at last month's World Twenty20 in Bangladesh.
"I was confident (of getting the job)," Giles told Sky Sports on Sunday.
"I went into the interview and thought I had as equal a chance as anyone else, if not a better chance having been close to the team and known what the systems are and, at the same time, not really had full control.
"I can't go into too much detail about that process, but I'm bitterly disappointed I didn't get the job," the former Warwickshire left-armer, who subsequently coached the Midlands side to the 2012 County Championship title, added.
However, Giles insisted: "At no time or stage does that mean I wish anyone in that side any ill going forward. We all want England to do well."
England play their first match since Moores's re-appointment when they face Scotland in a one-day international in Aberdeen on Friday.