Hamilton's signing, which was announced by the Maranello team earlier this month, has left the Spaniard looking for a drive for next season and beyond.
Ahead of the launch of Ferrari's 2024 challenger on Tuesday, Sainz made it clear that the news was unexpected but conceded he'd had time to digest it, having found out before the world at large.
"There was, obviously, a bit of a surprise like everyone in the F1 world with the news," he said. "Everyone was surprised in a way with what happened.
"From my side, you can obviously understand that I got to know the news a bit earlier than anyone else.
PLUS: Can Ferrari's all-new chariot challenge for 2024's F1 honours?
"But it's true that then I had some weeks to reflect, some weeks to prepare and some weeks to also get ready for the car launch, for the first race of the season.
"So it gives you a bit of time to digest it, to take your own conclusions and to focus on the 2024 season there is ahead.
"But the fact that it was a bit of a surprise to the whole F1 world is no news, and it was obviously also for me."
Sainz said he had a lot of supportive messages on his phone after news of Ferrari's decision to drop him became public.
"Obviously, it's been busy, especially the last couple of weeks," he said.
"Well, first of all, a lot of messages of support and a lot of nice messages that I've received during my time in these last couple of weeks, which I would like to thank a lot of the F1 world and also friends back at home, that have been very supportive and very encouraging."
Last year, Sainz made it clear that he wanted to have his Ferrari future sorted out before the start of this season.
However, now that he's a free agent, he says he is in no hurry to make a decision on where he will be in 2025, making clear that it will be a crucial choice ahead of some of the "most important" years of his career.
"As much as I said that I wanted to have my future sorted before the first race, I think now there's things in this scenario [that] have changed quite a bit, as you can imagine," he said.
"So I think, it is going to be probably a longer process. We're going to have ahead of me probably my most important three or four years of my career, where I want to make sure that I am in the right place at the right time.
"I want to make sure I pick the right next destination for me. So I'm going to take my time to think about it, to listen to all the options, to have a look at all the options, so that I can just feel comfortable when I take the decision, [that] I've given myself enough time and with enough information.
"Having said that, I think it's completely possible to separate one thing and the other. I have a good management team that also will take care of that. So my full focus will be in Bahrain this year.
"And I'm going to start the season as strong as I can, putting all my effort in being quick, straight from the go. And yeah, the other thing will sort itself out as time goes by."
