The Serie A club confirmed on Saturday night that Acerbi, 25, had had an abnormal growth removed in a Milan hospital - a growth the player later revealed had been on a testicle.
After thanking fans and well-wishers for their messages of support, the former AC Milan and Chievo centre-half described the process of discovering he had a problem and how his new club helped him receive immediate treatment.
Last night, he wrote on his Twitter account: "Thanks to everybody who has written to me and to those who didn't but were thinking about me.
"I'll be back on the pitch soon and I'll be stronger than before."
And speaking to the Gazzetta dello Sport today, he added: "They were terrible moments. My first reaction was to shut myself away - I took my bike out and went for a long ride to take my mind off it.
"But thankfully I reacted well. I rang my girlfriend Valeria and my agent Andrea Cattoli. I shared my fears with them and the next day they accompanied me while I had an ultrasound in Milan.
"Their proximity to me was essential at that time, and thanks to the intervention of president (Giorgio) Squinzi everything was organised in a very short time.
"I had surgery around noon on Wednesday and I was discharged within 36 hours."
Newly-promoted Sassuolo - for whom Acerbi signed from Genoa earlier this month - have not yet put a time frame on the player's return to action as he recuperates at home.
"When you walk into the hospital you realise what's going to happen to you," he added. "The kindness of the doctors does not mask the suffering of those around you and your fears are magnified.
"The removal of a testicle involves quite a lot of pain post-operation - it's been no walk in the park.
"The pain is beginning to subside. I can walk okay and I've been out with Valeria to take my mind off it.
"And I've now told my mother Silvia. After I lost my father in March 2012 I didn't want to worry her before the surgery. Speaking out now is better for everyone."