Saunders lost his WBO super-middleweight title to his Mexican rival when he failed to come out for the ninth round, suffering serious swelling to his right eye resulting from a crunching uppercut from Alvarez.
The Brit, 31, was taken to hospital where he underwent surgery on Sunday and has now issued an update to fans on Facebook.
“Thanks everyone for the messages,” Saunders wrote.
“Broken eye socket and broken cheek bone in three places. Operation yesterday all went well.
“You win some, you lose some. Didn’t feel out of my league but got caught with a good shot and couldn’t see.”
Since Saunders was forced to quit on his school, rancor has raged among fans and fighters as to whether he showed a lack of heart by not continuing – especially as Saunders himself has previously questioned fellow boxers for not going the distance when injured.
In his statement, Saunders suggested the decision had been taken by his trainer, vowing he would make a ring return despite fears over the severity of his injuries.
“Ben [Davison] got the corner to pull it. Thank you to all who watched. I’ll be back, God bless you all,” Saunders wrote.