His side, who have been among the favourites to win the tournament since it began, were slightly disappointed in the group stage and were somewhat bailed out by their talisman.
The Barcelona star scored the winning goals in victories against Bosnia-Herzegovina and Iran, before netting twice in Argentina's 3-2 triumph over Nigeria.
Messi's goal against Iran was particularly memorable. After Argentina had toiled away for 90 minutes but failed to break through their opponents' defence, he shifted the ball onto his left foot and curled a majestic strike into the top corner from 25 yards out to seal the win.
But Sabella insists it is "normal" for a side to rely on their top player, and compared Messi to Brazil's Neymar in that regard.
"I think both players are amazing players," Sabella said. "Messi is the best in the world, Neymar is a great player, and of course with players like those the team depends on them."
He added: "It is normal, Argentina depends on Messi and Brazil depends on Neymar. It is normal."
With four goals each, Messi and Neymar are among the top scorers in this year's tournament, with only Columbia's James Rodriguez ahead of them on five.
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Messi has, however, played one fewer game than Rodriguez and Neymar, and will be looking to make some headway in the race to the Golden Boot when Argentina face Switzerland on Tuesday.