The Japanese driver, who raced for the Sauber team last year, was unable to secure a deal for the current season despite raising almost 8 million euros through a fundraising website.
Kobayashi instead joined Ferrari to compete in its World Endurance Championship GTE Pro programme.
The 26-year-old says his sights are still set on a return to grand prix racing, but admits he is frustrated by the trend to choose drivers based on their financial backing rather than their skill.
"At the moment, there are many teams who prefer to choose their drivers based on how much money they can bring, rather than on their ability on track," Kobayashi said on Ferrari's website.
"I hope this trend will change, because my aim is to be back there as soon as possible and I am working hard to succeed.
"Meanwhile, all I can do is give my all to Ferrari in the GT races and be available to the team for whatever they want me to do, such as events like this, or when they ask me to help with the development of the car by working on the simulator."
Kobayashi got behind the wheel of a Ferrari F1 car over the weekend for a demo run in Moscow, but the Japanese was caught out by the conditions and crashed against the barrier.
"The track was very slippery and there was a marked bump at that point, which is why I hit the barrier," he explained.
"A shame, but I am pleased the team let me out again after a few minutes."
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