Nicolas Gonzalez and Lautaro Martinez scored first-half goals in Lima on Tuesday, lifting Lionel Scaloni's men to a third win in four World Cup 2022 qualifiers.
Argentina extended their unbeaten run to 11 games, while they have won their past three away qualifiers – something they had not achieved since 2000.
Messi was pleased with Argentina's display, which came five days after their draw at home to Paraguay.
"Happy with the victory, we needed it after the game we played the other day," the star said, via Argentina's Twitter account.
#Eliminatorias 🎙️ Lionel Messi: "Contento por la victoria, la necesitábamos después del partido que hicimos el otro día. Desde el principio hicimos un grandísimo encuentro, llegaron los goles y creamos muchísimas ocasiones".— Selección Argentina 🇦🇷 (@Argentina) November 18, 2020
"From the beginning we had a great match, the goals came and we created many, many chances."
Messi added: "The second half the other day was already very good and I think we continued on the same line, even raising the level a bit.
"I think this is the way we have to follow. Little by little we are becoming stronger as a group."
Messi made his 142nd Argentina appearance against Peru, joining Brazil great Cafu for the equal fifth most by a South American man.
The six-time Ballon d'Or winner wants to continue contributing for Argentina, who won in Peru for the first time since 2004.
"Whenever I come here I try to do my best and I feel qualified to fight for this shirt," Messi said.
"I feel good to continue working and adding games."