The 26-year-old Sheffield native briefly held the silver medal position behind Norwegian gold medallist Oystein Braaten at Phoenix Snow Park after scoring 91.00 with an acrobatic and near-flawless routine.
He was ultimately overhauled in the third and final run, however, by runner-up American Nick Goepper and bronze-winning Canadian Alex Beaulieu-Marchand, despite another impressive score of 90.00.
Although praising his rivals for their "amazing" displays, Woods was left feeling a bit short-changed.
"It's all good, I know what's up. I know what I did. I stand by my word, I reckon my run was pretty badass," he told reporters of his high-risk but clean second effort.
"I knew that that 91 is not going to hold. It's kind of a little secret language between the judges," he added.
"I can put my hand on my heart and say that run, totally clean, I definitely could have won. I'm going to go back and watch the competition, but I was pretty sure I laced that run."
Woods, who finished fifth in the event at Sochi four years ago, also suffered a deep gash under his chin after kneeing himself during one of his jumps in the opening run.
He just missed out on a second slopestyle medal for Team GB, following Isabel Atkin's surprise bronze in the women's event on Saturday, the first British medal in a Winter Olympic skiing discipline.
It was still a great experience, said the enthusiastic Woods, and a decent crowd at the venue were treated to a "perfect show".
"If people are going to be inspired by skiing, then we couldn't have put on a better show," he said.
"And Izzy (Atkin) came away with some hardware."
(Editing by John O'Brien)
