De Vries was ousted from his AlphaTauri seat by Red Bull advisor Helmut Marko on Tuesday just 10 grands prix into his rookie season, in which he failed to get on par with team-mate Yuki Tsunoda.
AlphaTauri called on Red Bull's third driver Ricciardo to take the Dutchman's place, the Australian joining the Faenza squad on loan after impressing his parent team during a Pirelli test in Silverstone.
De Vries has since kept radio silence, but on Wednesday, eight days after his dismissal, he took to social media with a statement in response to losing his F1 drive.
He thanked Red Bull and AlphaTauri for giving him a chance in F1, but also expressed his disappointment at lasting less than half a season.
"A short note from me… After recent events, I decided to take some time for myself away from social media, which I will continue to do," De Vries wrote on Instagram.
"I would like to thank Red Bull and Scuderia AlphaTauri for the opportunity to live my dream. Of course, it hurts that the F1 chance I dreamed of for so long ended prematurely.
"But life is not a destination, it’s a journey, and sometimes you have to take the hard road to get where you want to be.
"I am grateful for our privileged lives, proud of our journey and my family. This is just another experience; we move on and look forward to the next chapter.
"Thank you to everyone for your kind and encouraging messages in the past week. It’s been heart-warming to feel your support."
Last week, Marko explained he pulled the trigger because he saw "no improvement" from 28-year-old De Vries, who was expected to match Tsunoda straight away thanks to his experience as a champion in F2 and Formula E.
"We contracted Nyck because he performed great at Monza last year," Marko told Dutch newspaper De Telegraaf.
"We expected him to be at least equal to his team-mate Tsunoda this year, but that was not the case. Actually, he was always three tenths slower than Yuki. We saw no improvement.
"We had to do something. Why wait, and what do two more races matter if you don't see any improvement? Nyck is a very nice guy, but the speed just wasn't there."
Ricciardo joins AlphaTauri from this weekend's Hungarian Grand Prix after half a season on the sidelines as Red Bull's third driver following his departure from McLaren at the end of 2022.
The 34-year-old Australian said he was excited to make his F1 comeback after taking some time off following his punishing two-year McLaren stint.
"There was no question that I was going to say yes," Ricciardo told F1 last week.
"Once I'd done a few sim sessions I started feeling like myself again. And that kind of brought me back to normal Daniel, where I was falling back in love and ready to go again."
