Norris's best time from across the two three-day tests at Barcelona last month ended up as the slowest lap in the combined standings, but his team-mate – Carlos Sainz – put McLaren eighth in the same order and sixth in the overall teams' classification.
Regarding the areas he considers the MCL35 to be strong and weak from what he had felt during testing, Norris said: "It depends what I compare to.
"I'm happy with [some] areas and how it's improved compared to last year in some areas.
"Some areas it's not moved on as much as what I would have liked. Areas it's not good at compared to Mercedes - [they] are the fastest - probably everything.
"I don't think there's any area where we're as competitive as Mercedes. [If I could] be harsh, I could say it's not good enough in any area, but in terms of progress, which is not easy to do in Formula 1, I'm happy. Obviously I'm not going to say the areas.
"But yeah, [I mean] more in terms of consistency of car from one lap to another [it's better], when the wind is not terrible, [so is] being able to push on the car in the long runs.
"The car is just a bit nicer to drive. It's less on edge - less peaky, let's say. It's a bit more stable and consistent.
"I'm still pushing - the limit still moves up, and I'm driving on that limit so the car is still a lot of sliding and moving around a so on.
"But the main thing is, and an easy way to say, it's just more consistent and nicer to drive."
When asked by Motorsport.com how happy he was with the new McLaren before heading to the first race, Norris replied: "So-so.
"I mean, things are good, I'm very happy with things and the progress we've made since [the first test]," he added.
"Because of all the things like the wind [which was strong during the days Norris drove at the second test], it's been very hard to get a good feeling of what the car is like.
"But I'm happy - I think we have an understanding at least of what the car is good at and what it's not good at. And those areas that we have to work I think it's very clear.
"So it's not easy and clear just to [say] how different those things [are] going to Australia.
"But we know those areas, which is a good thing - it's not like how or why. I think we understand that.
"As a driver, and comparing myself to this time last year, I'm a lot more confident and I feel a lot better.
"And that's a good thing - it makes me feel [like] I'm in a much better position because of that going to Australia."