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."
Source: Autosport