Messi's hat-trick at Kansas City Stadium saw him equal the all-time men's World Cup scoring record of 16 goals, drawing level with Germany's Miroslav Klose.
Earning his 200th cap, the 38-year-old became the first man to compete in six World Cups and the oldest to score a hat-trick in the tournament's history - exactly 20 years to the day since his first goal on the global stage.
While the victory was a boost to Argentina's hopes of successfully defending their title, Scaloni said there was no room for complacency.
"This team knows that anyone can beat us," he added. "If you get a little overconfident, any opponent can win. In this World Cup, strange and difficult things are happening. If we do things right it will be hard to beat us."
Scaloni attributed the victory to the squad's chemistry, noting that the bond between teammates is what pulls them through when things become difficult.
The result means Argentina have avoided the opening-match stumbles of their 2018 and 2022 campaigns and they now turn their attention to their next match against Austria in Arlington, Texas on June 22.
"There is a long way to go to try to reach the end," Scaloni said. "But it is always good to start by winning; that undoubtedly strengthens everything."