Whelbourne led early on and was lying second as the race pace hotted up but, with three laps remaining, the 22-year-old from Nottingham lost his footing and fell to the ice ending his medal dream and hurting his ankle in the process.
Canada's Charles Hamelin, who had won Whelbourne's semi-final, took gold at the Iceberg Skating Palace in two minutes 14.985 seconds with China's Tianyu Han claiming silver in 2:15.055 and Victor An taking bronze for host nation Russia in 2:15.062.
Whelbourne, who will be assessed ahead of the men's 1000m on Thursday, said: ''Unfortunately a block got under my foot and I toed in, which has given me a twisted ankle but we don't know how it is.
''It can be quite common in the sport. The block move, we have seven and up to eight people racing with tight-knit overtakes, so it happens quite a lot and this time it happened to me, unfortunately when I was in my best form.
''I am really pleased with my performance today.''
Whelbourne had been quickest in the heats with a time of two minutes 14.091 seconds and then followed it up with another impressive showing in the semi-finals to go through to the showpiece as second fastest.
In the women's short track, British hopefuls Elise Christie and Charlotte Gilmartin both came through their respective 500m heats with few problems.
Christie was wary of her draw on the outside in heat two, but was glad to win her race ahead of Russia's Sofia Prosvirnova and get through to the quarter-finals in an event she admits is not her priority.
She said: ''Sofia is a good skater, she has been in the finals of World Cup this year and I haven't made the final in the 500. But it was a good chance to work on everything I wanted to work on. I used this to warm up and work on the last few things because the 500 is not so important to me, so I am using it to build to the other two events.
''I had a lot more speed in me, definitely. I was being patient and watching what I was doing.''
Gilmartin, who finished second in her heat to also qualify for Thursday's quarter-finals, was simply relieved to get her first race out of the way without mishap.
She said: ''Me and Elise both had lane four which isn't the best lane but we both got the job done."
Great Britain's men's curling team made a winning start to their campaign as they saw off hosts Russia 7-4.
David Murdoch's rink of Scots went in front in the second end of the round-robin fixture, opening up a 2-0 lead, before the Russians - cheered on by a vociferous crowd at the Ice Cube Curling Center - pulled one back in the fifth.
GB responded by surging 6-1 ahead in the following end, and although their opponents reduced the deficit, they were unable to save themselves from losing a contest in which skip Murdoch had 100 per cent accuracy.
GB's next fixture is Monday evening's clash with world champions Sweden, who got their campaign under way with a 7-5 victory over Switzerland.
Murdoch said: ''We will see if we can take that momentum into tonight. Niklas Eden and the guys are world champions, they had a win as well so it will be a tough game."
Great Britain's women were also in action and lost a difficult round-robin opener against reigning Olympic champions Sweden 6-4.
Eve Muirhead's all-Scottish rink, playing opponents they had beaten to become world champions last year and lost to in the subsequent European Championship final, found themselves 3-0 down after three ends but battled back well, securing a point in each of the next three to draw level.
The Swedes then regained the lead with two in the seventh and, after GB replied to make it 5-4 in the eighth, Margaretha Sigfridsson's rink completed the job by claiming another point in the ninth.
Earlier Chemmy Alcott gave her confidence a boost for the downhill event on Wednesday with a decent run in the super combined.
The 31-year-old used the downhill part of the event as a practice run for Wednesday and did not compete in Monday afternoon's slalom.
Alcott always had the intention of pulling out of the super combined following the morning's downhill, as she is wary of taking on too much after the third leg break of her career in August almost stopped her from competing at her fourth Winter Games.
The Londoner said: "I want to focus on the downhill in two days. I have to think about where my strengths lie this week and they definitely lie in the speed disciplines. I know that I can ski better than that, so the downhill should be pretty great.''
Alcott was the fifth person out of the blocks at the Rosa Khutor Alpine Center but was delighted to put down a time of one minute 44.83 seconds, which left her in 16th place.