The actor told Zap2It that he had never expected the show to have such a big American fanbase.
"I was just in New York," he said. "Me and Karen [Gillan] and Steve [Moffat], we were overwhelmed by the enthusiasm.
"I thought there was not a Doctor Who community in the US but it's got legs here. It's truly been an exceptional response that not any of us can fathom."
Smith also confessed that he was touched by the fans' response to his first full episode 'The Eleventh Hour'.
"It inspires humility to see how they've embraced that first episode," he said. "I think that there are better episodes coming, actually, which is exciting."
Doctor Who continues on Saturday at 6.20pm on BBC One in the UK and on Saturday at 9/8c on BBC America in the US.