Ryding, the first Briton to finish on a World Cup podium since Konrad Bartelski's second place at the Val Gardena downhill in December 1981, led after the first leg but was unable to match Hirscher's second run, losing out by 0.76 seconds. Russia's Alexander Khoroshilov was third.
"If the season stopped now, I'd be over the moon....I'll just keep trying, that's all I can do," Ryding told Austrian television.
Ryding, whose previous best performance was seventh place in Zagreb in January, clocked 53.42 seconds on the first leg, giving him a lead of 0.29 seconds over Italy's Stefano Gross.
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Hirscher, overall World Cup winner for the last five seasons, appeared to have given himself too much to do as he was 1.02 seconds behind but charged down the course in just 50.79 seconds on his second run to take the initiative.
Gross skied off the course near the top and Ryding managed to improve on his first leg with a timing of 52.57 seconds but still missed out.
(Writing by Brian Homewood in Berne, editing by Neil Robinson)
