The 32-year-old won bronze behind Mayer and Swiss Beat Feuz in his title defence at the Jeongseon Alpine Centre while his team mate Aksel Lund Svindal, the 2010 champion, was fifth.
With compatriot Kjetil Andre Aamodt having won gold in 1992, 2002 and 2006, Norway had won five of the eight Olympic super-G titles, including the last four coming into the Games.
"It's a little special that you would keep that thing going but I think this is more the normal way," Jansrud said after adding the bronze to the silver he won in the downhill.
"You try. Sometimes you succeed and sometimes you don't. I wished I skied a couple of tenths faster today."
Aamodt's success in Salt Lake City and Turin made him the only skier, male or female, to have successfully defended an Olympic super-G title.
Jansrud said he always thought it was a big ask to go back-to-back even if he was the leader of the super-G World Cup standings.
"I thought I will not defend the title unless some of the other guys are also making mistakes, and then you know in the start field that people do rarely make mistakes," he said.
"I think halfway through I skied good and then I started making a few mistakes, so coming out with a bronze medal is a very good day.
"I was obviously aiming for the gold and wanted to really attack it but it didn't happen and then I guess you have to accept that."
Svindal, who ended Norway's 70-year wait for a downhill champion on Thursday, had a good run but a wobble as he approached the line cost him and he finished half a second behind Mayer.
"I'm a little disappointed for sure because you know you are racing for the gold," he said. "But I mean I had a great day yesterday."
The 35-year-old, who fought back from a series of serious injuries to race in Pyeongchang, said he had been fatigued after his gold medal-winning exertions but refused to blame that for his performance.
"I mean you're really tired, but you're also really inspired, so it was all good," he said.
Jansrud's fifth medal drew him alongside Alberto Tomba and Lasse Kjus in third place on the list of most decorated Olympic Alpine skiers.
"Massive being mentioned in the same sentence as my biggest idols when I was a kid," he said.
"Even though a lot of people expected a Norwegian gold, this is more the normal way in Alpine skiing, where the margins are tiny."
(Editing by John O'Brien)
