For many observers in F1, the pace of the RP20 has been eye-catching this season, and if it proves legal following a protest from Renault, then it is likely to be pushing Mercedes and Red Bull at some circuits.
After finishing third and fifth in the opening two races of the season at the Red Bull Ring, Norris recognises he has been fortunate with the results, notably in the Styrian Grand Prix on Sunday.
Sergio Perez, who had started from 17th on the grid, was challenging Red Bull's Alex Albon for fourth late on when he damaged his front wing.
As Renault's Daniel Ricciardo and the second Racing Point of Lance Stroll tangled over one another, and due to the damage to Perez's car, Norris managed to make up three places in the final three laps to score another superb result.
"We had a little bit of luck with Perez on the final lap," said Norris. "I don't know what position he started, but he was a long way behind, and he would have finished way ahead.
"The Racing Points are way too quick for us. When someone extracts all the pace out of the car like Sergio, then I think he showed how fast their car is.
"I'm not really expecting that we have much of a chance against them when they don't make mistakes.
"But like the previous weekend, we made the most out of our opportunities, with Stroll and Ricciardo battling and making mistakes, and I gained on them, and then with Sergio and his front wing."
Norris is fully aware of McLaren's position in the current pecking order, particularly trailing a car continually described by team principal Andreas Seidl as "a one-year-old Mercedes" given its resemblance to last year's title-winning W10.
"I think we maybe have the fourth-best car, maybe the fifth, but the top three [Mercedes, Red Bull, Racing Point] are nicely ahead, and obviously Ferrari didn't run," added Stroll, referring to the collision between Scuderia team-mates Sebastian Vettel and Charles Leclerc on lap one that led to them both retiring.
"We've had a good first two weekends of the year, but I think they're probably going to get tougher from now on."
GPFans is a multi-platform, multi-language brand dedicated to Formula One coverage. We bring you all the ins and outs of the sport, 24/7, everything from up-to-the-minute news and features to the latest viral stories and clips.
We believe that a new generation of exciting, outspoken drivers will make F1 more popular than ever before, and we want to give our users access to as much of their heroes as possible, on and off the track. From Lewis Hamilton to Max Verstappen, Daniel Ricciardo to Sebastian Vettel, we provide in-depth analysis of every every Grand Prix in the season, from Australia to Abu Dhabi.
With Formula One under the new ownership of Liberty Media, how the sport is being covered is evolving, and GPFans will look to be at the heart of this progression into new media, as one of the fastest-growing sites covering the king of motorsports.