Norris jumped Ferrari's Charles Leclerc at the start to lead the first half of Sunday's United States Grand Prix. But he was powerless to keep Red Bull's Max Verstappen from a 15th season win and also had to let Lewis Hamilton's Mercedes past in the closing stages.
Afterwards Norris was promoted back to second when Hamilton was disqualified for excessive plank wear, meaning the Briton has now finished second in three of the past four races.
And while Norris said Sunday was "still an amazing day for us" given the progress McLaren has made, he felt that his best chances of sealing his maiden grand prix win in 2023 have now come and gone.
"Do I think our best chances have gone? I would say yes," Norris said. "I think Qatar was our best chance of winning a race. And I missed out on that one.
"I don't want to say no, I don't say like never. I think there's no super high speed, Suzuka-style, Qatar-style circuits left which is where we're strong."
He added: "I don't think they're any good ones for us coming up. I think our best have gone.
"I just want to be hopeful that we can do good results and I think we can still fight for podiums but these guys are too quick for me."
Norris is basing his assessment on McLaren's Achilles heel, its persistent weakness in low-speed corners, which could bite it in all four remaining races in Mexico, Brazil, Las Vegas and Abu Dhabi.
"If you looked at the GPS overlays of how bad we are in the slow speed [areas], I'm not looking forward to Brazil," he explained.
"I think we're going to be pretty shocking there. Vegas and Abu Dhabi are probably the better ones."
Norris was visibly struggling in Austin's Turn 11 hairpin, locking up his front-left on Lap 25 before relinquishing the lead to Verstappen.
According to team principal Andrea Stella that slow left-hander provided further proof that the Woking squad's low-speed woes have not been cured, which will have to wait until the 2024 car.
"Braking into Turn 11 and then traction out of Turn 11 was the most problematic phase from a car performance point of view," he explained.
"It was no surprise, it is to do with bumps and with braking and traction in two very low-speed corners, where we said already that we know the car doesn’t perform very well.
"It has been addressed in development but there is no turnaround in this season to fix this."
