"It's been a sad week and everyone was down spirits so I tried really hard to get a good result and maybe put a smile on people's faces. Although everything is going on, try and find some good feelings for everyone," she said.
Robinson said the conditions were perfect in Andorra with the mountain surface holding up.
"It was just really good conditions. It's didn't break up. I was starting last on the first run and there was hardly any bumps or anything. Normally a lot of surfaces deteriorate a little bit and this one was really good. It was perfect.
"I've been skiing really well in training so I was really excited about putting it into a race. Unfortunately it's the last event of the season and it starts up again in October so I can rest of a little bit and get ready for the next season."
The event featured the season's top 25 skiers. World Champion Petra Vlhova of Slovakia was third.
The New Zealand prospect got her first career podium when just six months older than Shiffrin was getting her first top-3 finish, in a December 2011 slalom.
"It's an amazing feeling," Robinson told Swiss broadcaster RTS. "It's crazy, so cool to share the first podium with Petra and Mikaela. They're such great skiers."
Shiffrin had plenty of praise for Robinson.
"She did amazing skiing in the first run and she backed it up with a really amazing performance and now she has her first World Cup podium. That's super cool.
"It was the perfect day for her to be able to attack like that and the conditions were amazing, everything was just right there and she took advantage of it and her skiing was awesome. It was really really cool."
It's been a whirlwind few months for Robinson, who represented New Zealand at the Pyeongchang Winter Olympics as a 16-year-old.
She will head home to Queenstown after four months on the road next week to resume her schooling.
Shiffrin's 17th World Cup race win this season also extended her own record for men and women. At age 24, her 60 career wins trails only 26 behind Ingemar Stenmark's all-time total.
The American star needed only a top-15 finish on a sun-soaked day in Andorra to ensure closest challenger Petra Vlhova could not overhaul her points total.