France's Maurice Manificat won the gold medal with a time of one hour 17 minutes 47.3 seconds— narrowly beating Roland Clara of Italy who came second at 1:17:48.0.
Norway's Sjur Roethe took bronze in 1:17:49.0.
Babikov, who was the top Canadian, finished with a time of 1:17:55 but was in the top three and in contention for a medal just past the race's half-way mark.
"There were two guys on the breakaway and I thought I would get with them and maybe we'll stay away from the group but it didn't happen. I tried. What can I say?," said Babikov, 32, who was born in Russia.
"I just didn't have enough energy today."
Graham Nishikawa of Whitehorse finished 15th, Calgary's Kevin Sandau was 34th and Brian McKeever, also of Calgary, was 38th.
It was the best finish of Nishikawa's career and the best of the season so far for Babikov.
"I got some bonus points which is not usual for me and 12th place is still awesome," Babikov said. "I hope we'll have more World Cups here."
National coach Justin Wadsworth said Babikov wasn't feeling well before the race but added that he has the ability to ski with anybody in the world on his best day.
"He just hung in there. The result was good. He's been solid," Wadsworth said. "I think the biggest improvement is Ivan's been so consistent this year. For sure he's been close to the top 15 in distance races so that's a really good start for him."
Canada ended up the weekend with three top-10 finishes, including Canmore's Chandra Crawford who finished sixth in Saturday's final.
Wadsworth, who decided to rest Alex Harvey and Devon Kershaw for Sunday's skiathlon, thought the weekend could have gone better.
"I would have gone back to Devon and Alex to give us our best results. A podium, I thought was really a potential," he said.
"We didn't get what we wanted but these home World Cups are good for really our young skiers because we don't get to race against this calibre of field very often."
Earlier in the day, Poland's Justyna Kowalczyk won the women's 15-kilometre skiathlon in 42 minutes 51.5 seconds.
Finland's Anne Kylloenen won the silver medal in 43:26.4 and Norway's Vibeke Skofterud took bronze in 43:26.5.
Whitehorse's Emily Nishikawa finished 34th in 46:30.7.
"I'm really happy. I had a great race and I was thrilled to get into the 30s," said Nishikawa, 23, who is the younger sister of Graham Nishikawa.
"I think I'm one step closer to my goal of getting into the top 30 and then top 15 and it's a good start."
Other Canadians included Daria Gaiazova of Banff, Alta., who was 37th and Frederique Vezina of St-Ferreol-les-Neiges, Que., who finished 43rd.
Crawford finished 46th after making the final in the women's 1.3 kilometre sprint on Saturday.
"I knew it was going to be tough and super hard and scaling mountains out there. I grew up doing that and it doesn't get any easier," said Crawford.
Crawford, the 2006 Olympic gold medallist, said not only did the team's strong performance Saturday move her into the top 30 for the first time this season — it was doubly good news for her and training partner Perianne Jones of Almonte, Ont., who finished 11th in the 1.3-kilometre sprint.
"Perianne called me because we both made the Olympic criteria so she's now had two top 12 results and I've had a top six and that's pre-selection for Sochi," Crawford said.
"It was really important to do something good yesterday to set up this next season, to qualify for world championships which are in Italy in February so the weekend was just a blast."
It was the second gold medal of the World Cup in Canmore for Kowalczyk, who also won the women's 10-kilometre race on Thursday.
Her fans were waving Polish flags and singing the national anthem as she raced across the finish line.