The 26-year-old opened the event, paired in the first group with Tsubasa Hasegawa of Japan.
Grieg was quick to start, and looked to be getting the better of Hasegawa, before the Japanese skater pushed ahead.
It came down to the wire, with Hasegawa finishing just narrowly ahead with a time of 35.08 seconds.
“I was happy with that,” Greig said. “It was tough to skate first but that was a much better race for me than I’ve done all season.”
The Netherlands-based athlete went into the race hoping for a top ten finish, but his final result -- 21st out of 36 -- was still an Olympic Personal Best.
Norway's Havard Lorentzen won the gold in a time of 34.41. Lorentzen inched out local skater Kyu Min Cha by 0.01 seconds who won silver, followed by China's Tingyu Gao (+0.24) in bronze.
Greig was +0.81 off the pace, and with less than one second separating the top 26 skaters, the podium finish could have been anyone's.
“At the end of the day I wasn’t far off my goal because it was such close results,” he said. “And if I could have just finished a little stronger I would probably have got there.”
His Olympic campaign is not over yet, with the 1000m event to come on Friday (February 23).
“I’ve actually been doing better at the 1000m this season so I’m looking forward to that,” Grieg said.
“The ice feels good, the venue is fantastic, so you can’t ask for much more.”