The first instalment of the drama, which also stars Benedict Cumberbatch, aired in America on Sunday.
"I hope it will [get] a similar reaction to what it's been in the UK, which is extremely positive and extremely favourable," Freeman told New York Magazine. "Even more than we could have wished for. It's beyond our wildest dreams, really."
Freeman admitted that some viewers may be unhappy with the fact that the Sherlock Holmes stories have been placed in modern times.
"Sherlock, in the Victorian and Edwardian times, used every bit of possible technology known to him, so that's what ours is doing," he explained. "It's not really a differing principle. I imagine there would be some people who are reticent about that stuff, because I think I was myself when I heard it was going to be modernised. I thought, 'Oh hello, that could be bad TV'."
He continued: "[But] it was some of the best writing I had probably ever read for television. I loved it... I hope that Americans go with it, because the most important thing about the Sherlock Holmes stories isn't the frock coats. It's the essence of what he is, and the essence of what the [Holmes and Watson] relationship is. And chasing bad guys."
Sherlock continues in the US on Sunday at 9pm on PBS.