The comment came in the wake of their 2-0 win over Kenya in Cairo on Sunday in their opening game at the tournament in Egypt, where Mahrez scored the second goal, and inevitable questions from reporters afterwards about his potential talismanic role for the team.
"I do not like highlighting players. We need to put a little less focus on Mahrez if we want to make this a big tournament for us," Belmadi responded.
Mahrez, 28, is competing at a third Cup of Nations for his country, who were quarter-finalists in 2015 but flopped in the first round two years ago despite being one of the pre-tournament favourites.
That made Sunday's comfortable win over Kenya pleasing for Belmadi -- who like Mahrez has a Manchester City connection, having played briefly at the club in 2003.
"It means a lot to win the first match in any competition," Belmadi said. "We used to start poorly, it was always difficult for us to start well at the Africa Cup.
"In our history, most of the time, we often lost the first match, so this is also a message to the players that we can go far."
The game against Kenya had been a test of their ability to overcome obstacles, he said.
"Everyone has had difficulties in this tournament," added Belmadi. "We knew about this Kenya team, they were very well prepared. We knew their strengths and weaknesses. Without downplaying what Kenya did, I think we were good."
Algeria share the Group C lead with Senegal, who they meet next in Cairo on Thursday.
"We expect a tough match against Senegal, the tournament favourite. It's a challenge we have to take on," the coach said.
(Reporting by Mark Gleeson; Editing by Sudipto Ganguly)
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