Ranieri was only appointed in June on a two-year deal but the Italian is set to depart after just one campaign with Nantes 10th in the table heading into the final match of the season.
"We can't hide anything. We had a meeting with the sponsors, he thanked everyone," Kita said.
"He has to be thanked for all the work he has done.
"It has not always been easy, there are regrets, but this is life and there is no anger."
Nantes were challenging for European qualification until they faded late in the season, with Ranieri's men a point adrift of ninth-placed Montpellier and two clear of Guingamp ahead of Strasbourg's visit on Saturday.