The actor said he was “just trying to move forward with my life” and felt “lucky” to be at home with his family for Christmas.
Cinematographer Ms Hutchins was killed after a prop gun went off on the Rust film set in New Mexico.
In a video posted to his Instagram Baldwin said he looked forward to “some aspects” of the incident being behind him.
“I wanted to take a moment to say thank you to all those people who sent me such kind words and best wishes and strength and hope and prayers and so forth,” he said.
“So many great sentiments from so many people, I got hundreds of emails from friends and family and colleagues and people… to send me strength and good wishes.
“I am very grateful for that.”
Referring to the incident in Santa Fe, he continued: “I’m looking forward to some aspects of this being behind me, of course for everyone who’s involved in this it’s never going to be behind us because someone died so tragically.
“I never lose sight of that, not a day goes by that I don’t think about that.”
The actor said being with his wife and children was “the only thing I care about”.
“(I’m) just trying to move forward with my life and trying to get through a tough time, a really tough time,” he said.
I’m looking forward to some aspects of this being behind me, of course for everyone who’s involved in this it’s never going to be behind us because someone died so tragically.
“I feel very awkward, going through this it’s been very difficult and I want to say happy holidays… whatever holiday you’re celebrating.
“I hope you are as lucky as I am in one department and that is to be home with your family.
“I don’t have anything smart or original to say, just thank you to these people who sent me good wishes.”
Signing off he added: “Be safe, wear a mask, get the booster and don’t let Santa down the chimney without a mask.”
US authorities recently issued a search warrant for Baldwin’s mobile phone in the ongoing investigation into Ms Hutchins’s death.