"It was hard times, especially the last two to three years," he said, adding that the pain has prevented him from training over the summer.
Kostelic was also second in the slalom at the 2010 Vancouver Games and he became the first man with four Olympic silver medals overall in Alpine skiing.
"I'm a 'Silver Surfer,'" Kostelic said. "Actually, it's funny, because way before this time, my gaming nickname was 'Silver Surfer,' so probably I made my own destiny. ... People on the podium have changed, and I stayed there."
Kostelic's younger sister, Janica, won four golds and two silvers at the 2002 and 2006 Games. Since she retired in 2007, Janica has helped her brother in a coaching role.
"This is the 10th Olympic medal in our family, and this fact makes me very proud," Kostelic said.
Innerhofer said he never trains slalom and so he said he was thinking "there will be no chance" for a medal.
"Unbelievable. Un-be-liev-a-ble!" said the demonstrative Italian, who jumped onto the podium with a backflip.
The super-combined medalists were determined by adding the times together from one downhill run and one slalom leg.
Downhill leader Kjetil Jansrud of Norway finished fourth.
The temperature soared to 13 degrees Celsius (55 degrees Fahrenheit) shortly before the start of the slalom leg.
Norwegian standout Aksel Lund Svindal finished in a tie for eighth with former overall World Cup winner Carlo Janka of Switzerland, and French contender Alexis Pinturault went out toward the end of his slalom leg -- one of many racers who struggled with a difficult course set by Kostelic's father, Ante.
In all, 11 racers did not finish their slalom legs, with several of them looking downright foolish as they lost control and tumbled down the mountain head over foot.
Information from The Associated Press was used in this report.