Norris made the comment in the wake of a controversy after qualifying in Singapore, when Max Verstappen escaped lightly with just a pair of reprimands rather than grid penalties for impeding incidents in qualifying.
One involved blocking Yuki Tsunoda on track, which the stewards determined was largely down to the Red Bull team not giving its driver enough information.
The second resulted from Verstappen waiting at the end of the pitlane to create a gap before heading out on track, holding up a queue of cars in the process.
The reprimands came as surprise to rival teams, who usually expect grid penalties to result from such incidents.
Pierre Gasly insisted after the Singapore race that he will ask the FIA in Suzuka weekend to explain the lack of a harsher punishment for Verstappen, and Norris has also expressed his frustration.
"I don't want to say too much, because I'll just create controversy," said the McLaren driver when asked by Autosport about the Verstappen case.
"But I think the blocking one on track was the one that should have been a penalty. He blocked someone.
"It's not just down to the team. I know the team got the fine in the end of the day, but it should be down to the driver as well to look at his mirrors, and see if someone's there.
"You've got nothing else to do the whole lap but look in your mirrors, and it seems like a lot of people struggle to do that."
He added: "I think there should just be harsher penalties for blocking people, because so many people do it. It ruins your lap it ruins your qualifying, it put Yuki out in qualifying, and he was P1 in Q1.
"Just no one seems to care enough. And it's happened a lot this season, it's happened to me quite a few times, especially with certain teams.
"But it's also up to the driver to look in the mirror, they [have] got nothing else to do but hit the recharge button and look in your mirror. People seem to struggle to be able to do that and in F1, which is a surprise."
Lewis Hamilton and Charles Leclerc agreed that the drivers have to keep an open dialogue with the FIA about penalties.
"I obviously I was in the pitlane when everyone stopped, and I couldn't see what was happening up ahead," said Hamilton. "We always push and work as closely as we can with the FIA to have consistency and there is some variation, so we have to continue to work on it."
Leclerc added: "I was a bit surprised. Especially the one in the pitlane, because that could open quite bad situations in the future.
"But again, as Lewis said, it's always an open discussion with the FIA, and trying to explain to them what our point of view is and, and improve. And I'm sure we'll have that discussion tomorrow evening at the briefing."
Verstappen himself downplayed the controversy about his escape with reprimands and said all he had done was give his side of the story.
"Every single instance is different," he said. "The only thing I can say about Singapore is that I explained what happened when I was sitting in the car, and the information that was given to me, and that's the only thing I can do. And then it's up to the stewards to make that call."
Albon unhappy with Perez penalty
Alex Albon questioned another incident in the Singapore race, in which Sergio Perez received a five-second penalty for turfing the Williams driver off the road, costing him a valuable eighth place.
Albon thought that the punishment could have been harsher.
"I think it's quite a tricky one," he said. "I think consistency, we push on it a lot of drivers, and I think as teams as well and viewers as well. But it's a tricky one.
"For example, you can take my incident with Checo when he has a five-second penalty. It's consistent with everything else. But is it really fair? Maybe not. So I do think there needs to be flexibility in some ways."
