Biles had been bidding for a fourth gold in Paris on the final day of competition but after slipping off the balance beam earlier errors also proved costly on the floor.
But the 27-year-old insisted she could not be disappointed by her medal haul in the French capital including three gold as US teammate Jordan Chiles snatched bronze.
"Rebeca's so amazing, she's queen," said Biles.
"She's such an excitement to watch and then all the fans in the crowd always cheering for her, so it was just the right thing to do.
"It was an all-black podium so that was super exciting for us but then Jordan was like should we bow to her and I was like absolutely."
Biles' crowd-pleasing acrobatic floor routine to Taylor Swift's hit song "Ready For It" included two of the skills named after her.
But a 0.6-point deduction for twice stepping out of bounds proved costly as she scored 14.133, narrowly behind Andrade's gold-winning score of 14.166.
The Brazilian, already a gold medallist in the vault at the pandemic-delayed Tokyo Games in 2021, won her fourth medal in Paris after all-around and vault silver and team bronze.
Despite finishing fourth in the balance beam earlier, Andrade picked herself up to "show people it's possible".
"It wasn't about beating Simone but beating myself," said the 25-year-old
"It was very cute of them. They are the world's best athletes and what they did means a lot to me, we're always rooting for each other, the final is very difficult for everyone."
Andrade said she was proud of the all-black gymnastics podium at Olympics after the world championships, to "show black power again, we can make it happen".
"I love myself, I love my skin colour, but I'm not focused on that. Rebeca goes beyond her colour. The same goes for Simone and Jordan."
Biles also finishes the Paris Games with four medals after winning golds in the team, all-around and vault.
Her Olympic total now stands at 11 -- seven gold, two silver, and two bronze.
Her well-publicised troubles with the debilitating mental block known as the "twisties" led to her withdrawal from multiple events in Tokyo three years ago.
Chiles, 23, took bronze after initially placing fifth after a review upped her difficulty score and pushed Romania's Ana Barbosu off the podium into fourth.
Barbosu was in tears as she had been unfurling the Romanian flag to celebrate.
"I was so tired, I didn't realise my coaches had put in an enquiry but when it came through I was very proud of myself," said Chiles, who also won team gold.
