"I think at a certain point at the end of last season, maybe there was not the sort of trust and confidence and respect - on both sides - that you should be counting on for the development of the team and driver," he told Britain's Sky broadcaster.
"It's like with your girlfriend or wife -- sometimes when you disappoint too much, you know the relationship is just ... broken," added Abiteboul.
Nonetheless, Abiteboul said it is possible Kovalainen, 31, will continue to work with Caterham in another capacity.
"We continue to have discussions with Heikki to see if a different project could be possible," he said.
"Let's be honest: we'd be keen to keep experience in our lineup. That's something we'd both be interested in under the right conditions."