Messi played his fourth full game of the month as Luis Suarez's goal saw Barca salvage a point at the Wanda Metropolitano on Saturday.
Days after scoring a brace against Las Palmas, Messi played two games for Argentina — including scoring a hat-trick in Ecuador to lead his nation into the World Cup.
After his side's draw with Atletico, Valverde said Messi was fatigued, but he praised the forward for what he could bring to Barca — even when below his best.
"I agree that Leo is tired after the games he's had to play, but we know he'll always respond in any situation," he said.
"We know how much fear he instils in the opposing players and fans."
The draw ended Barca's perfect start to the La Liga season, but they still sit five points clear at the top.