A major upgrade package introduced over the past two races helped Norris produce a star performance on home ground at Silverstone last weekend.
The young Briton qualified on the front row and briefly led the opening stages before coming home in second place behind race winner Max Verstappen and ahead of Mercedes’ Lewis Hamilton.
The scale of McLaren’s progress has left rivals hoping they too can follow suit and deliver a similar leap forward in performance with in-season car developments.
But Norris has urged caution about reading too much into the Silverstone performance, and even the fact that the McLaren seemed to be much better in race trim than it has been earlier in the campaign.
Although the improved tyre management on display at the British GP hinted at genuine progress, he said that the MCL-60 was still far behind rivals in critical areas.
Asked by Motorsport.com about the improved tyre management on display at Silverstone, Norris said: “It's definitely not been present in the car all season and Bahrain was quite the opposite.
“These tracks allow us to look after the tyres well. We're very, very competitive in high speed and we're almost on par with what Red Bull could achieve. And actually, I would say, towards the medium speed like Turn 15 here, Stowe, I would say we're close to being the best car on the grid.
“Super, super high speed like Turn 9 [Copse], maybe not quite so much, but that was in qualifying and then when we come to the race, we definitely maintain our performance when others seem to take a bit of a hit.
“In doing so we can actually look after the tyres pretty well, especially when there's no thermal limitation within the tyre like there was necessarily here.”
Pondering the strengths and weaknesses of the McLaren package, Norris said that there remained a major issue in slow turns – which is where Hamilton was able to put him under some pressure in their battle.
“We do have a poor car, and when I say poor, I would say pretty terrible, in the low-speed corners,” explained Norris. “It’s extremely difficult to drive.
“I feel [people] getting excited and I accept that, but we're going to go to a couple of tracks coming up where I'm sure people are going to be saying: “What have you done now? How has it got so bad all of a sudden?”
“So, we've improved a lot of things like tyre degradation, and there's always little things you try and do with tyre cooling and blah, blah, blah, but nothing big from that side. It's just this track has allowed us to look after the tyres nicely, and keep them in a good condition. It is as simple as that.
“A lot of it is track-specific. I don't want to get too excited. Good things have come from the upgrade but there's still plenty of things which are a miles away from competing in certain places with a Mercedes, and as a whole package competing even with a Red Bull. So, a lot more work to be done from both of those areas.”
The clear weaknesses in the McLaren package are why team boss Andrea Stella is looking forward to the challenges of the next race in Hungary – as the tight-and-twisty Hungaroring, which often boasts good weather, will perfectly expose problems.
“In a way we look forward to Hungary, to check more comprehensively where we really are,” said Stella.
“There's not as much high speed, and if anything, it is a low, medium speed dominated track. Also, you can have hot conditions, which is again, another testing territory for us.”
