"Unfortunately Charles won't be with us this season," fellow Frenchman Abiteboul told Infosport+, "but I want to thank him for the job he did for us last year."
Pic was strongly backed in F1 by Idec Groupe, Lagardere and even Renault, and so presumably his successors at Caterham have arrived with even more lucrative sponsorship.
Abiteboul also hinted that performance may have been an issue, saying Pic "has some talent which can develop in a larger, more mature team".
Caterham, however, is the only remaining team in pitlane yet to announce its 2014 drivers.
The logos of McGregor, the sponsor of Pic's 2013 teammate Giedo van der Garde, have been removed from Caterham's official website, suggesting that the team will enter 2014 with an all-new driver lineup.
International reports say the most likely 2014 pairing is Kamui Kobayashi alongside rookie Marcus Ericsson.
Britain's Sky, the Reuters news agency, and France's RMC said Caterham is expected to confirm its new drivers on Tuesday.
RMC added that Pic, having worked until now with Olivier Panis, is now being managed by Jacques Villeneuve's well-known former manager, Craig Pollock.