Norris beat Red Bull's Max Verstappen in Sunday's Miami Grand Prix after a mid-race safety car allowed him to take the restart in the lead, but the Briton still managed to drive away from Verstappen to take a convincing maiden win.
After 109 races without finding the top step of the podium, Norris' breakthrough win was long overdue, but the 24-year-old says he never doubted his day would come even if he felt others did.
"I've had my moments where we've been close and I've never been able to convert it into the win," Norris said.
"As much as a lot of people doubted that I was going to be able to put it together and win a race, I wasn't worried.
"I've been more confident than ever this year that I've got what it takes and the team have got what it takes and I was patient with it.
"I've just been doing my job and executing my races, executing my qualifying, and doing what I can do best. I knew my time was coming."
Norris previously had a close call in 2021's Russian Grand Prix, when a botched strategy in the rain call saw him and the team throw away a potential win.
That near-miss, which Norris felt "a lot of people talk crap about", provided questionable arguments to those that doubted the Briton that he could cope with the pressure of racing for wins.
"People like to continue to use that, even after China last weekend when I made a mistake in Turn 1 on Lewis [Hamilton]," he added. "Anyone can say what they want. People don't need to like me. They don't need to support me.
"But when people doubt me in certain situations, you want to go out and prove them wrong.
"They think they know what they're talking about and when you prove that they don't, then that's a nice thing to go out and do.
"It's not a dig at anyone, but it's just nice to just go out there and do my job and show people what I'm capable of.
"I wanted to say like the Valtteri line ‘to whom it may concern’, but I was like ‘ that's copyrighted’, so I didn't want to repeat it!"
