He told Sky Sports News: "After what happened yesterday in qualifying, today was all about damage limitation for me, so I'm as happy as I can be with a P2 finish.
"I have had the pace in the car all weekend here but I wasn't able to capitalise on that, so getting second place from a bad weekend is pretty good, I guess.
"The guys did a fantastic job today to get us another one-two and the fans here in Austria have been insane. Next race is in Silverstone and all the positive energy from my home fans, it will be a special time and I'll be going all out for the win."
The result leaves Hamilton 29 points behind the German in the drivers' championship.