Bottas has twice been given team orders this season, told to stand down from attacking Hamilton in Germany before his strategy was altered to assist Hamilton in Italy as the Finn backed Raikkonen into his team-mate, shredding his countryman's tyres in the process.
When Arrivabene was asked why Ferrari had not given similar orders to Raikkonen to boost Vettel's title chances, the Ferrari boss said he "hired drivers, not butlers" a clearly pointed message towards Bottas.
With Hamilton having moved 30 points clear of Vettel in the drivers' standings, Arrivabene says his comment came in the heat of the moment, claiming Bottas had understood his motives.
"As soon as I said it in the heat of the battle, I knew it would create controversy," Arrivabene told Autosprint.
"Since then I have exchanged messages with Valtteri Bottas. I wanted to apologise to him and understand what I meant.
"It had slipped out but it's not a label I want to use for Bottas. I appreciate his response very much that he understood."
Arrivabene stood by Ferrari's decision not to favour Vettel in their home race, despite it opening the door for Hamilton to win and extend his championship lead.
"I just instructed them to not do anything stupid," Arrivabene added. "It was said that Kimi did something unfavourable to Sebastian, but what should he have done?
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