Curtis said: "I'm shell-shocked with a feeling of massive regret.
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"Manager Kenny Jackett only spoke to me for two minutes and said he wanted to bring his people in, but that's his prerogative after the year he's had."
During his time at the club Curtis has been community officer, youth team coach, assistant manager, caretaker manager and head of youth development for the south Wales side.
Curtis has now been offered another role with the club will meet with chairman Huw Jenkins this week for discussions before deciding whether to remain at the club or look for a move elsewhere.
Curtis added: "I'm not sure what the position is yet but would guess it is something in the hospitality section of the new stadium.
"I've got to work through my options and get over the disappointment. I would like to remain at the club in some capacity."