The defender was withdrawn late in the game after he was the victim of a nasty challenge from Nabil Fekir.
United scored a goal in each half but three unanswered goals from the Spanish outfit was enough for them to claim victory at the Loughborough University Stadium.
Marcelo Bielsa's side took the lead after six minutes when a well-crafted move saw new signing Junior Firpo find Patrick Bamford in the box for the striker to nod a header across the goal.
Betis, managed by former Manchester City manager Manuel Pellegrini, hit back after 10 minutes when Aitor nipped onto a loose pass from Stuart Dallas and was forced wide by Diego Llorente but he got his shot away which went in off the post after looping towards goal via a deflection.
Leeds had named a strong side for the contest, with their opening game of the Premier League season at Manchester United just two weeks away.
Raphinha had a shot well saved by Rui Silva with 17 minutes gone before Betis, who have faced Wolverhampton Wanderers and Derby County in their pre-season schedule, took the lead five minutes later.
Alex Moreno got past Raphinha on the left and found Aitor who provided an expert touch to lay the ball off for Borja Iglesias to finish from the centre of the box.
Bielsa made a first-half substitution after the goal as Jamie Shackleton was introduced in place of Llorente who was brought off as an injury pre-caution.
The clubs had agreed to allow four substitutes before kick-off, with a fifth allowed in the case an injury.
The Leeds manager made more changes at half time with Mateusz Klich and Patrick Roberts coming on for Firpo and Bamford, respectively.
Klich had an early chance to draw Leeds level but his curling effort was safely gathered by the Betis goalkeeper on 51 minutes.
A mistake from Illan Meslier gifted a third to Betis as Sabaly's ferocious cross was spilled into the net by the Frenchman.
Leeds responded almost immediately when Klich latched onto a defensive error from the Spanish side and finished expertly into the bottom corner.
Struijk was then forced off late on following a nasty kick from Fekir. Betis thought they had sealed the win when Aitor tapped home from close range but he was denied by the offside flag.
Camarasa had a chance to claim a fourth goal for the touring side but was denied by a good save from Meslier. Rodrigo came close to adding a late third goal but his shot was blocked by a defender with the goalkeeper beaten.
Leeds are set to play Ajax on Wednesday and Villarreal a week today before kicking off their competitive campaign against Manchester United on August 14.
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