He has made a great start in Milan this season after signing from Chelsea, scoring twice in the 4-1 Serie A thumping of Cagliari at the San Siro on Sunday.
France playmaker Kylian Mbappe said that finding sleep will be difficult for him as his side bowed out of the ongoing Euro 2020.
Benzema's replacement, Olivier Giroud, scored a late double in the final seven minutes to secure victory for the world champions after Antoine Griezmann had opened the scoring in the 29th.
Mendy now faces a race against time to put himself in contention for a place in France's Euro 2020 squad.
Despite the goal drought, Deschamps stuck with the Chelsea striker, who featured in all of France's seven matches at the World Cup, and Giroud is happy to have played his role.
Under Deschamps, France focussed on utility football and getting the job done instead of grabbing eyeballs.
Pogba caused a stir on Sunday when he told reporters this summer's World Cup could be his final one because you don't know what can happen tomorrow.
Deschamps's side, who face Denmark on Tuesday eyeing top spot in Group C, registered just four shots on target all game against Peru.
France will next play Denmark, who are second in the group after drawing 1-1 with Australia in the earlier game, in their final game on Tuesday.
Didier Deschamps' side now faces Denmark on Tuesday with top spot in Group C up for grabs but progression to the next stage assured.
With their title rivals failing to fire, France have vowed to ramp up the intensity and put their stamp on the World Cup with victory over Peru.
The 27-year-old Griezmann has scored 21 international goals, including five during France's run to the Euro 2016 final.
Didier Deschamps has told France they must do better after escaping a humiliating draw with Australia in a 2-1 World Cup opener.
Pogba endured an inconsistent Premier League campaign, scoring six goals and providing 10 assists in 27 appearances.
The phoney war is over and most of the big guns have arrived in Russia ahead of the start of the World Cup on Thursday.