Raducanu had promisingly broken in the first game of the third set and then saved a break point on her way to going 2-0 up.
However, Badosa, the world number 62, worked another break point in the sixth game and the Briton succumbed with a double fault.
Raducanu, who is 89th in the world, failed to take three break points in the next game and, on the back of that, lost her serve to fall 5-3 behind.
With Badosa serving for the match, the 21-year-old found the line with a backhand to save a match point as she broke her opponent.
It was only a temporary reprieve as Raducanu let a 40-15 advantage on her serve slip in the next game and, facing match point, served a double fault.
Raducanu was out for eight months – during which time she had operations on both of her wrists and her left ankle – before returning to the tour in January.
She turned down the chance to play for Great Britain at the Olympics because she did not want to switch back to playing on clay at Roland Garros.
Instead, Raducanu has prioritised hard courts the forthcoming US Open – the tournament she won in 2021 as a qualifier.
Alexander Zverev defeated Carlos Alcaraz in sensational fashion to make it through to semi-finals of the ATP Finals in Turin on Fr
Rohan Bopanna and Matthew Ebden. (File Pic - Mike Stobe/Getty Images/AFP Photo) Rohan Bopanna of India and Matthew Ebden of Australia concluded their partnersh
India’s Rohan Bopanna and Australia’s Matthew Ebden ended their partnership on a winning note after defeating Germany’s Kevin Krawietz and Tim Puetz in th
Key eventsShow key events onlyPlease turn on JavaScript to use this featureFirst set: *Zverev 2-2 Alcaraz (*denotes next server)I turn my attentions back to Tur