After 110 grand prix starts and 16 podium finishes, McLaren driver Norris won his maiden F1 race on Sunday after he benefitted from a safety car period following a collision between Haas' Kevin Magnussen and Williams driver Logan Sargeant.
Norris was running fourth when his main rivals began to make their first and only pitstops, which they made before the safety car was deployed.
The McLaren driver, leading after his rivals had stopped, was able to pit and rejoin still in first place thanks to early leader Max Verstappen being slowed by the safety car.
Ferrari's Sainz was another of the drivers who did not benefit from the safety car, and he felt he "could have won" the race had he pitted a lap later.
But according to the Spaniard, the "lucky" circumstances did not detract from Norris's victory, as the Ferrari driver felt the Brion was fully deserving.
"I think luck comes to the guys who deserve it," said Sainz. "Lando is one of those guys that deserved a little bit of luck this weekend to win his first race.
"Between us drivers, we know who deserves to win races and who is driving at the level to win races. And we all know Lando has been driving to win races. And when he gets finally won we're all happy for him," Sainz added.
Sainz, who was Norris's team-mate at McLaren during the 2019 and 2020 seasons, said his friend and rival had been driving like a race winner for some time now.
Norris had finished on the podium twice this year, including a second-place result in the Chinese GP.
"In F1, there's just this luck factor that Lando got and won a race," Sainz said. "But he's been driving like a race winner for many, many races in a row now. And he just deserves that win. Luck no luck, doesn't matter.
"He's a race winner. And it was about time that it was coming for him.
"And people just need to accept that when you don't have the best car, sometimes you need a bit of luck."
Norris himself admitted in the post-race press conference it would have been difficult to win the race without the free pitstop: "It would have been tough. I would have had to overtake two Ferraris, a Red Bull, Oscar [Piastri]."
Three-time champion Verstappen, who was second behind Norris in Miami, interrupted the Briton to add: "I mean, it's always if, if, if, right? If my mum had balls, she would be my dad.
"So, yeah, it's how it goes with racing. Sometimes it works out for you, sometimes it doesn't."
