The British driver produced a superb drive to beat home hero Verstappen into a distant second at the Dutch Grand Prix with a huge gap of 22.8 seconds separating the pair.
The result also cut Verstappen's lead to 70 points in the race for F1 world champion, but Norris stressed that this was still a huge gap to bridge.
"I've been working hard the whole year, and I'm still 70 points behind Max, so it's pretty stupid to think of anything at the minute," the 24-year-old told reporters after the race.
"I just take one race at a time, and just keep doing what I'm doing now. There's no point to think ahead and think of the rest," he added.
The McLaren has recently had a major upgrade that has improved performance and allowed Norris to outpace Verstappen all weekend from practice through qualifying to race day.
McLaren now has "100 percent" the fastest car, Norris said, adding that he felt the team had left some points out on the track over the season.
"We probably should have won two, three more races as a team, but we didn't... We should have won and we didn't, and it's because we've not done a good enough job. I didn't do a good enough job," he said.
The F1 circus heads next to Ferrari's home track of Monza in Italy and Norris predicted a very different race there.
"It's still a long way to go, so we still have to keep working hard... Monza is a completely different circuit, so we'll keep our heads down and keep chipping away."
As for Verstappen, he is suffering his longest lean spell without a race win since 2020 but said there was still a long way to go despite "not the best weekend" at home.
"That happens, right?" he quipped to a reporter who asked him whether he was concerned at a winless streak that stretches five races back to June.
"I've had a lot of good years. Some people have never won a race in their career, so you can also look at it like that," he said.
Verstappen started the season the way he finished his utterly dominant 2023 term, winning seven races out of the 10, but his form has since dropped dramatically.
This weekend was "just a bad weekend in general" but the last few races "haven't really been fantastic, so that is in a sense alarming."
"But we know that we don't need to panic. We are just trying to improve the situation, and that's what we are working on," said the three-time champion.
