The 23-year-old, who started 12th, collected two points in only his second grand prix.
"My start was very bad, I was a little bit safe into turns one and two," he said.
"Obviously we were a bit lucky with the Renaults, but I'll take it," added Albon, who moved up the order when Renault's Nico Hulkenberg and Daniel Ricciardo retired from scoring positions with three laps to go.
The points meant Toro Rosso have scored in both races to date this season, with Russian Daniil Kvyat finishing 10th two weeks ago in Australia.
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The British-born son of a Thai mother and British father, Albon finished third overall in the Formula Two championship last year.
Set to race for Nissan in the all-electric Formula E series, he was handed his Formula One shot after Red Bull promoted Pierre Gasly from Toro Rosso to its senior team and dropped Brendon Hartley.
He is only the second Thai driver since Prince Bira to race in Formula One.
"I enjoyed myself out there and it was good to get that experience,” he said of his second weekend.
"I’m very happy to pick up my first points in Formula One and I hope we can carry this pace into (the next race) in China."
(Reporting by Abhishek Takle, Editing by Alan Baldwin)
