A devastating fire at Le Constellation bar in the Swiss ski resort killed at least 40 people and injured 119 others.
Bodies continue to be identified and a criminal investigation is under way.
“We can’t imagine how it is, but it’s for sure terribly hard,” Rast told BBC’s Ski Sunday.
“I hope they will find the support with their family and everybody around. And I hope that the sport will bring a little smile on their face.”
Rast finished a close second to Shiffrin in the previous World Cup slalom event in Austria but was not to be denied a second time, making sure the World Cup’s greatest skier could not add to her record tally of 106 wins in all disciplines.
Shiffrin was just 0.1 seconds behind leader Rast after the first run, but set an imposing time in the second that opened a 1.69secs lead over the rest of the field.
But Rast went even faster to beat Shiffrin into second place.
“I know Shiffrin is really fast and I had to be really, really fast to beat her. I saw her start and I was like ‘mmm, OK, that’s good, that’s really good’, but I just tried to give my best, and it worked,” she said.
There are two more World Cup slalom events – in Flachau, Austria, on 13 January, and Spindleruv Mlyn in the Czech Republic on 25 January – before the Winter Olympics begin in Milan-Cortina on 6 February.