The Briton and his team-mate Daniel Ricciardo have had a disappointing start to the season, with the new MCL36 lacking grip and leaving them adrift of the frontrunners.
But with both drivers ending second practice for the Australian Grand Prix inside the top 10, Norris feels that the team has turned a corner from the dire situation it appeared to be in at the season opener in Bahrain.
"It looked alright - it wasn't amazing but it was decent," said Norris, who ended up eighth overall in the Friday evening session.
"It was probably our best Friday so far, so I'm hoping it will continue tomorrow because we have a good feeling.
"I think we have made a few changes and we have learned a bit this weekend from the previous two weekends that we have implemented, and it is working reasonably well.
"It is a small step forward, so it is a good start, and hopefully we can continue that into tomorrow and make further improvements."
Norris has no doubts, however, that much of McLaren's improved form in Australia is down to track characteristics – with the lack of slow speed corners not punishing it as much as they did in Bahrain.
"It is just the track, but of course there'll be some little things that we are improving - and little is maybe one tenth," he said.
"It is not going to make us half a second quicker or one second [quicker]. We are extracting everything out of the car and I think we are doing a good job.
"But a lot of what you are seeing is just the track, which is a good thing.
"Hopefully Bahrain was just a very bad one and I think we have understood a little bit more and hopefully more of the tracks are like here and Saudi.
"We are going in the right direction, but we are still a long way off."
McLaren team boss Andreas Seidl reckons however that not all of McLaren's improved form since Bahrain is down to circuit layout, as he believes the team has a better understanding of its car too.
"From my point of view, it was probably a 50/50," he said.
"When we look back at how the Bahrain test went and the Bahrain race weekend, we had so many challenges.
"We were definitely on the back foot going into the Bahrain race weekend, and we still had to take tick a lot of boxes that we wanted to at the test at the first race weekend.
"But then we obviously could apply all these learnings for the second weekend.
"That definitely helped to have a smoother weekend in Jeddah to extract more performance from the package.
"But then I guess also the track layout was definitely suiting our car more and that's why we would have been more competitive."
But despite the signs of progress, Seidl says work is ongoing at its factory to bring improvements that are necessary to get it closer to the front.
"We are obviously flat out back home with a clear plan of how to bring more performance to the car," he said.
"The most important thing was that we understood how we can get more performance to the car.
"We have a clear plan in place now, after the analysis of how we want to achieve that and when. We simply need to execute against this plan.
"It will take a bit of time. So you need to be patient while at the same time, obviously be ambitious, and bring these upgrades as quickly as possible.
"And in parallel, obviously, we try to score as many points as possible with the current package."
