Farah fell to the ground shortly after completing the race and was taken away from the finishing area in a wheelchair but later allayed fears for his health.
"I feel good," he told a news conference. "I don't remember passing out, but I think it was just I tried so hard in the race, obviously, taking a fall and then going through.
"I'm all right. It's fine. It's no big deal."
The Briton, who won the same half-marathon in 2011, endured a tough run after taking a painful fall after five miles. He recovered to finish in 61 minutes 50 seconds - 18 seconds behind Mutai.
Farah, who won the 5,000m and 10,000m golds at the 2012 Olympics and 2013 world championships, is preparing to run his first full marathon in London in April.
"The conditions today were very, very cold," he said.
"London's going to be different. But I feel good. I felt good at that point, to the point I went down."
Farah said his fall took a lot out of him.
"(The) last four miles, I was just pretty much seeing stars... everything was kind of blurred to me," the 30-year-old said.
Asked if the fall was the difference between him winning and finishing second, Farah replied:
"It's hard to say. I've not watched the race, but I know, when I went down, I went down quite hard. I did feel like my hip, got caught on my hip, my ankle, the whole right-hand side...
"When I went down, there was a massive gap, and it was hard to close that gap again," Farah added. "I tried my hardest and gave 110 percent. That's all you can do."
He and Mutai will meet again on April 13 in the London marathon, which will be Farah's next race.
"Nothing changes," he said. "Training's been going pretty well, but at the same time, it would have been nice to come out here and win the race, but Mutai is a strong athlete."
Mutai's countryman Stephen Sambu finished third to round off a good day for Kenya in New York, with their compatriot Sally Kipyego winning the women's event.
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