Norris saw both of his Q3 laptimes deleted in Friday's qualifying at Losail, meaning he would start the race from 10th rather than second behind polesitter Max Verstappen.
In Saturday's sprint shootout, Norris then went off track in the final corner of his second flyer while on a pole-worthy run, instead getting demoted by team-mate Oscar Piastri.
Piastri duly won Saturday night's sprint race from pole, while Norris recovered from 10th to third in Sunday's grand prix thanks to McLaren's rapid pace on its favoured high-downforce Losail circuit.
Norris was hard on himself after his qualifying mistakes, saying "I am so sh*t sometimes" on the team radio on Friday because he felt he should have been able to fight for not one but two victories in Qatar.
"I don't know how much quicker Max could have gone in qualifying, but I guess if I want to be honest with myself, I should have fought for two pole positions this weekend and potentially two victories," he said.
"I know it's a big thing to say, but if I just did a better job and didn't make the mistakes ... which is why I've been so frustrated. Because I knew what was on the cards, what we were able to potentially achieve and that was [two] victories.
"So, I feel like it was a weekend of missed opportunities for myself to take the fight to Max and at least give ourselves that opportunity.
Source: Autosport