The Frenchman, who was appointed trainer of the North Africans in February 2016, was speculated to be considering leaving the Atlas Lions before the tournament and Friday's penalty (4-1) shootout defeat to Benin appears to have heightened exit reports.
The recent disappointment follows Morocco's group stage exit at the Fifa World Cup in Russia last year.
"I would like to say, in this very painful moment for all the Moroccan football lovers, thank you to the players who have been exceptional throughout the long period," Renard said in a statement released on social media on Friday night.
"To tell them that I love them and that you should only remember the best of our adventure.
"Thanks to all those who have worked for our success.
"I also thank all fans who have moved to Egypt, Russia, to all those who have supported us all along this road in Morocco and elsewhere.
"You've been a wonderful supporter. Football is made of joy and sadness. That's why we love [it] so much."
Renard, who won Afcon with Zambia and Cote d'Ivoire in 2012 and 2015 respectively, holds an enviable record in the competition as he has lost only three of 27 matches supervised.
In 2016 and 2017, the 50-year-old was linked to Algeria and Ghana's coaching jobs respectively and most recently in April, he was reported to be in the running for the managerial role at French Ligue 1 club Olympique Lyonnais.
"I have been in Morocco for three and a half years, but now we have to go home and think about the future," Renard said at the post-match press conference after Friday's game.
He has previously coached Ligue 1 sides Sochaux and Lille.