Norris qualified second and briefly led the British Grand Prix before finishing second behind Max Verstappen, while his team-mate Oscar Piastri started third and finished fourth after losing out to Lewis Hamilton under the safety car.
While acknowledging the Silverstone result and the leap in performance since the first part of the latest upgrade package was introduced in Austria, Norris insists that the team is not getting carried away.
"I don't think anyone has a spring in their step at all,” he said when asked by Autosport if he’d noticed a change in the camp. “We also know it's not going to happen that often at all.
"So we enjoyed the moment for sure. But we know we're not competing for wins or even podiums. We were close to that very often. It's a lot of things went right for this [result] to happen. Even though we should have had a P2 and a P3.
"I think the confidence came from knowing that we took a good step in the right direction. I think that's just where people gain confidence, that we were able to improve the car in some of those areas.
"But I don't think anyone's got overconfident in any way. I hope not.
"I do feel like we're in a better position now with our understandings, with the people we have, our areas of focus,” he said.
"The upgrade we brought to Austria is the biggest upgrade as a team McLaren has brought in the last five years.
"In terms of having a car, trying to find improvements with it over the year, it's the biggest improvement we've ever had in my experience of being with McLaren. That's a fact.
"And even prior to that, until they probably had the B-car in 2012 or something, when they had some other issues and things like that.
"So it's the first time we've been able to really bring an upgrade that's genuinely taken us a big step forward. So I have more hope than I have had over the last few years.”
Despite McLaren's recent upgrades delivering a significant step in performance, Norris admits the car is "still just as difficult to drive" as it has been all year.
"For me at the minute - even with this upgrade we've had, the performance - driving the car the handling has not gotten any better,” he noted.
"It still is just as difficult to drive, as difficult to execute qualifying laps with, in essence slightly easier because for a given mistake, we're actually still higher up there, especially over the last few weekends.
"And almost in the highest speed corners it's harder to make a mistake because the car's performing better.
"For me and where we've been over the last five years we've made the car quicker obviously, I don't want to get too ahead of ourselves, we've only had two weekends where we've been quick.
"But we have yet over the last five years made that step improvement in slow speed handling and drivability, disregarding load and absolute grip, let’s say.
"So for me, a bigger step would be improving how we drive the car, how easy it is to drive the car, rather than just adding 10 more points of load in slow speed, because that's only going to get us so far up the order."
