"Privately, Paula is very upset," a source told RadarOnline on Thursday.
"She's never going to admit it publicly but this stung. Paula likes Ellen and she doesn't want to say a negative word about her and she won't."
Fox announced on Wednesday that it had tapped DeGeneres to replace Abdul -- who last month used her Twitter page to announce that she would not be returning as a judge for the show's ninth season.
"I think Ellen will b a gr8 judge on Idol," wrote Abdul in a Twitter posting on Thursday. "She is wildly funny, talented and I wish her the best of luck!"
While Abdul reportedly rejected a $5 million a year offer to continue serving on Idol's judging panel, she still apparently believed that "a last-minute deal" could be worked out, according to RadarOnline, which added by that time Fox executive had already "moved on."