Whitten was tied for third with Australia's Annette Edmondson heading into in the fifth event, the scratch race, but the Edmonton native's sixth-place finish combined with the Aussie's win in that event made it nearly impossible for Whitten to move back into a medal position.
"I have no regrets," Whitten said while fighting back tears. "I've loved this journey. And I've experienced success and disappointment, and a bit of everything. I mean, that's part of sport."
The omnium is a six-event competition, spread over two days, and awards the gold to the athlete with the lowest point total.
Laura Trott of Great Britain won gold with 18 points, while Sarah Hammer of the United States took silver with 19 and Edmondson clinched bronze with 24.
Whitten posted the eighth-best time in the time trial, the final event, and finished with 37 points.
In the 3-km individual pursuit earlier on Tuesday, Whitten placed third with a time of 3:31.14, just behind Hammer (3:29.554) and Trott (3:30.547).
Whitten entered the second day of the omnium in fourth place after finishing eighth in the Monday's third event, the elimination race.
Britain's Hoy wins 6th gold
Chris Hoy set the British record with his sixth Olympic gold medal, defending his title in the keirin to finish off a dominating track cycling program for the home nation.
Britain won seven of the 10 gold medals awarded to match its haul from the 2008 Beijing Games.
Hoy was briefly overtaken by Germany's Maximilian Levy on the final lap of the eight-lap race, but pulled even with him on the final corner and out-sprinted him to the line.
Levy settled for silver, and Simon van Velthooven of New Zealand and Teun Mulder of the Netherlands were both awarded bronze when a photo finish could not decide third place.
Hoy became the first person to defend a keirin gold medal, and matched teammate and Olympic time trial champion Bradley Wiggins with seven overall medals.
Meares beat Pendleton in women's sprint
Anna Meares of Australia spoiled the British party at the London Velodrome by winning the Olympic gold medal in the women's sprint with a 2-0 victory over rival Victoria Pendleton.
Meares, who lost to the British rider in the semifinals four years ago in Beijing, denied Pendleton a third gold medal, which would have made her the most successful British female athlete at the Olympics. Pendleton has said she will retire after the London Games.
Guo Shuang of China won the bronze medal with a 2-0 win over Kristina Vogel of Germany.