In the wake of Norris and team-mate Oscar Piastri finishing behind race winner Max Verstappen at Suzuka, the Briton came on the team radio and said: "Double podium. We are coming for Red Bull."
But while the Japanese GP was another encouraging weekend for the Woking-based squad in its push to get back to the front of F1, McLaren team principal Andrea Stella is more cautious about expectations for the rest of the season.
While he is delighted with the progress that has been made through 2023, he thinks that Red Bull, especially with Max Verstappen at the wheel, is not yet within touching distance in pure pace terms.
When asked by Motorsport.com about how far away he felt Red Bull was, Stella conceded: "Still a step too far. But in fairness, at the moment, it looks [as if] Max is one step too far.
"There's a variability of tracks left in the season, but none of these tracks has the Singapore characteristics.
"While there could be some tracks in which we could be competitive - I think Qatar should be a decent track for us - I'm afraid that the characteristics we like, they are also the characteristics where Red Bull will be just outstanding.
"So we'll have to be realistic that we'll need some situations to happen to be able to make the final step."
McLaren's competitive situation in F1 has turned around dramatically this season, with a programme of upgrades having helped it emerge as Red Bull's main rival right now.
But Stella knows that nothing is ever guaranteed in F1 and sees Aston Martin's current struggles as an example of how quickly things can change. Its Silverstone-based rival was a regular podium finisher in the first races of the year but is now having to fight hard to stay in the points.
Asked how mindful McLaren was of how quickly progress can stop in F1, Stella said: "Very mindful. Very, very mindful.
"And if anything, we are trying to be as rigorous as possible, from a development point of view.
"We want to ensure that we are not shortcutting any step, and we don't get to [a situation where we say] 'we need to develop faster'. Then you start to skip some methodical steps that we have applied so far.
"I think everyone at McLaren, especially the technical leadership, are very aware that the pace of development is already fast. And that's what we need to keep pursuing.
"Then we'll see, once we are in Bahrain next year, who's been able to develop faster. We saw with Aston Martin that over the winter, big steps are possible, or like with McLaren, that you can do it even during the season."