Lautaro Martinez's header two minutes before half-time settled Thursday's contest in Buenos Aires, where 'Albiceleste' extended their unbeaten streak to 25 matches across all competitions.
Peru wasted a chance to salvage a point when Yoshimar Yotun's penalty cannoned off the crossbar with 25 minutes remaining.
Messi reacted to Argentina remaining undefeated on the road to Qatar 2022 through eleven CONMEBOL fixtures, though it remains to be seen what he was referring to when mentioning the referee after Martinez had also gone down inside the area in the first half.
"Difficult match, difficult to play. A lot of wind, they were playing deep, leaving little space for us," Messi wrote via Instagram.
"The referee always does this when he referee's us, as if he does it on purpose. But well, three important points and we're close to our objective."