Norris claimed third place for McLaren at the Emilia Romagna Grand Prix in April, benefitting from a late error by Charles Leclerc that dropped the Ferrari driver back to sixth place.
Norris said ahead of the summer break that it “blows my mind” McLaren managed to score a podium given its early-season car struggles, the team having enduring a sluggish start in Bahrain.
But Norris ended the year as the only driver not racing for Red Bull, Ferrari or Mercedes to score a podium finish as the ‘big three’ teams dominated the first year under the new regulations.
Asked by Motorsport.com if it meant anything to be the only driver outside these teams to score a podium, Norris replied: “A little bit.
“A podium always means something. It means something to me, means something to the team. But one isn't enough.
“One is like, we got lucky, and all of this stuff. You want to feel like you deserve to be there every time and we deserved to be there for sure. We weren't quick enough to be there. We were kind of way ahead of where we deserve to be.
“But yeah, one time isn't enough for me. It's not a good enough job by the whole team.”
Despite Norris enjoying a successful season en route to seventh place in the standings, McLaren slipped to fifth in the constructors’ as it lost out to Alpine in the battle for P4.
Norris maintained throughout the season that his driving style was not well-suited to the McLaren MCL36 car, with its weaknesses being more noticeable on team-mate Daniel Ricciardo’s side of the garage. Ricciardo scored just 37 points to Norris’s haul of 122.
Norris said McLaren’s car issues this year aren't a “new thing” and that the team knew it had endured a “very tough season.”
He added: “We found it difficult. We've been quite up and down. We've had a weekend like [Abu Dhabi] where we've been quick. And then we were in Brazil, which was one of our worst weekends of the whole season.
“We've had one of the biggest lows, and then maybe one of the best highs of the year in the final two weekends.
“So [there is] a lot of understanding still for us, a lot of learning. But we need to take a step next year, we have to take a step.
“And I feel like everyone's putting in the effort to do so. Time will tell.”