"As soon as I said it in the heat of the battle, I knew it would create a controversy," Arrivabene told Italy's 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."
Some believe that Ferrari had no 'team orders' at Monza because Raikkonen had already been told he would not be driving for the Maranello team in 2019, but Arrivabene said that team orders at race starts is impossible.
"I just instructed them to not do anything stupid," he insisted.
"It was said that Kimi did something unfavourable to Sebastian, but what should he have done? What he did is exactly what Lewis Hamilton or Sebastian Vettel would have done.
"What happened with Vettel and Hamilton had nothing to do with team orders."
Vettel has been roundly criticised for his mistakes in 2018, which despite having the best car could cost him and Ferrari the world championship.
However, Arrivabene said that it would be "completely wrong to point the finger when there are still so many races to go".
"I answer for the whole team, so it doesn't matter who made a mistake - the driver or the team. Someone must answer, and this person is me," he said.
Vettel is second in the driver rankings with 226 points heading into Sunday's Singapore Grand Prix.