The Briton now has 13 career podium finishes without a win, equalling now-retired German Nick Heidfeld's record tally from 2005-11.
Heidfeld had eight second places whereas Norris now has seven, six of them this season.
While the McLaren driver has years of racing ahead of him to take a win and return the record to Heidfeld, he recognised that standing on the top step of the podium might not be imminent.
Red Bull's triple world champion Max Verstappen won Sunday's race for his record-extending 17th victory in 20 races this season and his team's 19th in the same period.
"Very good, couldn’t have gone much better, to be honest," said Norris of a race in which he seized second place into the first corner after starting sixth.
"P2 (second place) is as good as we can get nowadays and for the time being, but very happy for the rest of it."
Norris, who had started on pole position in Saturday's sprint race and also finished second, said there was no point where he felt Verstappen might leave the door open for him.
"Max always seemed to have an answer to everything, which is a shame. But fair play to him, he drove a good race, so yeah, tough, with the wind conditions and everything but P2 is a good result," he said.
Compared to where McLaren started the season, with three non-scoring races in the first five, a string of second places represents an astonishing turnaround for the former champions.
As Norris pointed out, since the team brought a major upgrade to Austria in July he has scored more points than any driver other than Verstappen.
"We've taken some massive steps forward and at the same time, considering we’re talking about fighting the Red Bull, I think it's still a very, very good thing, for what we've achieved this year," he said.
"We're talking about one of the best drivers in Formula One ever, in one of the most dominating cars.
"And for us to go from where we were in Bahrain (at the start of the season) to getting close and talking about fighting a Red Bull I think are very good signs for us. And we know we still have plenty more things to come next year."
