"I said we want to win three races and I'm still here. We want to win three races," the Italian told reporters after Sunday's Austrian Grand Prix, adding that he still felt it possible.
The Red Bull Ring witnessed the second race in a row without a Ferrari driver on the podium and the seventh Mercedes win of the campaign.
Dominant champions Mercedes also completed a year of pole positions, with Lewis Hamilton chalking up his seventh of the season before losing out to determined team mate Nico Rosberg in the race.
Arrivabene had said before the opener in Australia that he would be happy if Ferrari won three races and his statement looked more achievable after Sebastian Vettel's victory in Malaysia.
Four times champion Vettel was on the podium five times in his first six races for Ferrari and arguably should have been there again in Canada and Austria had circumstances not conspired against him.
In Montreal, the German had to fight from 18th place to fifth after a grid penalty and problems in qualifying and in Austria was robbed of third place when a wheel nut jammed on his pitstop.
"We were not that far (behind)," Arrivabene said.
"I have to say, Sebastian made a very good race. Mercedes are still stronger, we threw away one more time the podium for a stupid piece that we need to fix as soon as possible. For me it is not acceptable."
Ferrari chairman Sergio Marchionne said Vettel, whose team mate Kimi Raikkonen crashed on the opening lap in Austria but finished second in Bahrain, was delivering everything the team had hoped for when he joined from Red Bull.
"I think Sebastian is doing a phenomenal job. I'm incredibly proud of the kid," he told reporters before the race.
"I think the car is going to get better and better. Unfortunately we started late, which is unfortunate, so we are making up lost ground," he added.
"But I feel relatively comfortable that by the time we hit Monza (Ferrari's home Italian Grand Prix in September) we are going to be in a much stronger position than we have been in all season."
(Editing by John O'Brien)
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