Norris ended up fourth at the Red Bull Ring with Mercedes' George Russell and seven-time world champion teammate Lewis Hamilton finishing seventh and eighth after penalties were applied.
The two other Britons are well ahead of him in the championship standings, with Hamilton on 106 points and Russell 72 to Norris's 24.
Mercedes are also second in the constructors' standings and McLaren sixth but if you are only as good as your last race then Norris is smiling.
"We definitely had the upper hand of them this weekend," he told reporters.
"I would say every other weekend of the year they've been ahead, this is the first time we've been ahead of them so I don't want to say all of a sudden we're ahead of Mercedes.
"Austria's always been our best race of the season, our most competitive and most successful...but we did take a step forward.
"Silverstone is full of high-speed corners which have been a big strength of ours, maybe not so much straight-line braking, which is another.
"There's further upgrades to come so I would say there's good potential for us to compete against them again and for me to be the top Brit. That would be a pretty cool thing to do at Silverstone."
Norris entered Formula One in 2019 and has never stood on the podium at Silverstone with a best placing of fourth while Hamilton, the most successful driver of all time with 103 victories, has won the event a record eight times.
The McLaren driver will have a one-off Google Chrome livery on his car this weekend in a nod to the shiny McLaren that Hamilton drove for the Woking team from 2007 to 2012.
"That's what I grew up watching, it's kind of what I fell in love with," said Norris.
"It inspired me to be a Formula One driver because before that I was more into MotoGP and motorbikes, motocross and quad-biking."
The Briton was punished in Canada last month for unsportsmanlike behaviour by slowing behind the safety car to create a gap to Australian teammate Oscar Piastri before pitting.
McLaren's request for a review was refused but Norris was not downhearted.
"I think everyone knows I'm not (unsportsmanlike) so it doesn't affect me too much," he said.
"Everything I did was completely normal and correct and by the book. There's nothing which makes what I did unsportsmanlike.
"They (the stewards) have now set a new precedent of what is allowed and what is not, and quite a strict one... if they are consistent, there will be a lot of penalties coming up over the next months."
