The Brest midfielder was expelled from the team’s training ground in Doha, Qatar after he appeared in a live video on streaming platform Twitch, showing his rump.
Coach Djamel Belmadi has since handed a call-up to Montpellier forward Andy Delort as his replacement in the squad.
Belkebla is satisfied with the decision of the 43-year-old gaffer and has vowed to bounce back from the setback.
“There is obviously a real disappointment vis-à-vis myself. It's a bit of a nightmare to miss Afcon but basically, the hard part is that I disappointed my family, and the people who were happy to see me in Egypt with Algeria and also to have disappointed the Algerian people by this inappropriate behaviour,” Belkebla told Football France.
“Everyone was proud of me. It's terrible to disappoint them. And next to that, one also has the feeling of a little dirty his surname. The look on the people is important. So it's an accumulation, there is sports and family disappointment. I am in a difficult time. You have to be strong.
“I made a mistake. When you wear the Algerian jersey, things have a very different, much stronger range. We represent millions of people. There is inappropriate behaviour on my part. There is a nation and its image, so it is understandable that I am sanctioned."
Recalling the incident which led to his expulsion from Algeria’s camp he said: “As we saw on the videos that circulated: my colleague was playing his game network. He did not warn me that he was doing live streaming.
“I understood this at the end of the friendly match between Algeria and Burundi. In the shower, I have a teammate who came to me to explain that there was a big problem around me. I did not understand because until then, everything was going remarkably well in selection. He then explained the situation on the bus. And there, turning on my laptop, I became aware of the situation.
“Immediately, I wanted to go see the coach Djamel Belmadi to apologize, but my teammates (Mahrez, Brahimi, M'Bolhi, Guedioura and Feghouli) advised me to wait because this is never the best time. They went to see the coach to try to fix things.
“[Coach Belmadi] told me that he was really angry at the time. Afterwards, he told me we were all human, and that we made mistakes. He explained to me that he could not keep me in the band with what had happened.
“They [my teammates] told me they tried but I got a lot of support from them. They told me they would be there for me from beginning to end. This comfort touched me. And since I'm in France, I'm with them on the phone. They are good guys.
“I will do everything on the ground to prove that I deserve it, and win back the hearts of Algerians. What happened, it will remain engraved for life. But now, I have to focus on my goals. I want to show people that I made a mistake but that I have always been strong in my mind since I was a child. I apologized, I hope that the Algerian people will understand my disappointment, and accept my regrets.”
Next season, Belkebla will play in the Ligue 1 with Brest after helping them gain promotion to the elite French top-flight last term.
The North Africans kick off their campaign against the Harambee Stars on Sunday, June 23.