McLaren has struggled for pace since the Bahrain test, where the main focus was on resolving a brake cooling issue.
After a disappointing Sakhir race saw the orange cars finish 14th and 15th, the team didn't bring any updates to Jeddah.
However, having qualified a respectable 11th, Norris moved up the field in the race, helped by a pitstop under the safety car and some attrition ahead.
In the closing laps he battled for sixth place with Esteban Ocon, before losing out on the final lap and having to settle for seventh and the team's first points of 2022.
"I think it's massive for us," he said when asked by Motorsport.com what the result would do for the team.
"It's just for the motivation for everyone. We still have a lot of things to look forward to, it's not like we've had two terrible weekends and it's like, no one wants to smile. We can smile a little bit and we understand we have a lot of work to do.
"And there's a lot of progress we've got to make if we want to be anywhere near competitive to top teams, huge work. But we know that, everyone back in the factory knows that, and they're already working harder than ever on all of those things, and coming up with a lot of new things.
"We're just good, these things always help, and definitely getting some points today and P7 rather than just like P10 and one point.
"That extra confirmation of a P7 is good news, and considering I was fighting for P6 as well. So yeah, good for everyone here, good for the guys and girls and good everyone in the factory."
Given that the MCL36 featured no updates, Norris conceded that the change of venue was the main reason for the improvement in form.
"The difference to last week is the track," he said. "Apart from that we've really not changed much. But it shows how big of a difference [there is] to where the car can perform, and where the strengths and weaknesses are. So we still have a huge amount of work to do.
"And if we went back to Bahrain today, or next week, we'll be finishing in Q1 and last place pretty much again. So there's not a lot of positives in those terms.
"There's positives in terms of, if there are tracks like here, similar to Barcelona-ish, then we can look forward to those tracks to score some good points and be raceable and competitive.
"But I'm not confident if we went back to slower speed tracks, Monaco, and Bahrain and tougher tracks that we're going to be that competitive at all. So that's where we really need to work on."
Asked if Sakhir suggested that the team had a better race car than qualifying car, he added: "It's mixed. I would say today we could have been ahead of the Alpines. And yesterday, we had no chance of being ahead of them.
"Maybe it's a bit of [we] go forward a little bit, and they go backwards. I'm not too sure. But there's so many things we have to work on."