Raducanu made a strong start by breaking in the first game of the third set and saved a break point, putting her ahead at 2-0.
However, Badosa, ranked 62nd in the world, earned another break point in the sixth game, and Raducanu faltered with a double fault.
Ranked 89th globally, Raducanu was unable to convert three break points in the next game, leading to her losing her serve and falling behind 5-3.
As Badosa served for the match, the 21-year-old managed to save a match point with a backhand that found the line, breaking her opponent’s serve.
However, this was just a temporary pause, as Raducanu allowed a 40-15 lead on her serve to slip, and while facing another match point, she delivered a double fault.
Raducanu had been sidelined for eight months during which she underwent surgeries on both wrists and her left ankle, before making her comeback to the tour in January.
She opted not to compete for Great Britain in the Olympics, choosing to avoid a return to clay courts ahead of Roland Garros.
Instead, Raducanu is focused on hard courts as she prepares for the upcoming US Open, a tournament she famously won in 2021 as a qualifier.