McLaren finally introduced its first true performance upgrade of the 2023 season on Norris' car last weekend, which allowed him to qualify in the top four for both Saturday's sprint and Sunday's grand prix.
While McLaren benefitted from both Mercedes and Aston Martin having an off-weekend, Norris still produced a spirited drive to fifth, which became fourth after an additional track limits penalty for Ferrari's Carlos Sainz.
Norris was delighted with the result and McLaren's race pace improvements, although keeping the MCL60 on track was hard work.
"I was a bit nervous coming into the race, that the race pace was going to let us down today but actually it was better than I was expecting which was a good surprise," Norris said.
"It's still not great, Fernando [Alonso] was clearly quicker a chunk every lap, and I am almost crashing in every corner.
"But to be fifth [fourth after Sainz's penalty] shows we’ve made a good step forward, so I am very happy with that."
Norris explained that McLaren's upgrades to the floor, sidepod and engine cover had added downforce to the car, but hadn't cured the car's inherent handling traits that makes it so hard to drive for the Briton and his rookie team-mate Oscar Piastri.
"The car just goes quicker around every corner but the way you have to drive is exactly the same which is our next issue to tackle," he added.
"Things that we’ve been complaining about all year that are still the same but just at a higher level, so I feel I can be really confident if we can tackle these issues.
"I feel like they are letting us down a lot at the minute, so it is not just about downforce, it is about handling and how you handle the car. More technical things that we need to tackle and understand.
"When we do that, I am confident we can fight the quicker cars ahead of us."
Norris can still take a lot of confidence from the Red Bull Ring weekend to his home race in Silverstone, with the Woking team pushing flat out to roll out even more upgrades.
But while he stressed how pleased he was for the work that has gone into McLaren's upgrade push, he also cautioned the team not to get too excited just yet.
"100%. The car is quicker, it is quicker everywhere," Norris replied when asked if Austria was a confidence boost for the team ahead of its home race.
"It is just very difficult to drive still. If we had a nicer car to drive or one that was just a bit easier or had a bigger working range, then I think we can take another big step forward.
"Plenty of things to work on and I think we have more things coming, so I don’t want to get too ahead of ourselves.
"I think this has been our best race of the year so I will make sure I’ll let everyone in the team know that.
"But just keep our heads down and keep cool before next weekend."
McLaren CEO Zak Brown added his praise of the team’s upgrades and hopes it can use the momentum going into the British GP where both Norris and Piastri will run the updates.
"We were third-quickest team on merit really all weekend. So we’ve got to keep our feet on the ground. One race, and it's close, but it was a good result," Brown said.
"Oscar lost his front wing and he didn't have the upgrade. Let's see when he gets all the toys on the car for next week."
