Four-times World Player of the Year Messi failed to score and even squandered a clear scoring chance in stoppage time as the South Americans did the bare minimum to reach the last four for the first time since 1990.
But his mere presence on the field appeared to inhibit Belgium who were strangely cautious even when forced to chase the game after Gonzalo Higuain's early goal.
"I think Messi played really well, it's not just about scoring goals, it's about having possession of the ball, attracting three opponents and then giving the ball to a team mate in an advantageous position," Sabella told reporters.
"Each time he gets the ball, it represents hope for all of us and a threatening situation for our opponents. Regardless of whether he scores goals or not, his influence is decisive.
"A game has many aspects, apart from goals," he added. "When you have a player such as Messi, who never, or almost never, loses the ball, it's water in the desert and not just when he scores.
"In the other game (against Switzerland), he gave a great pass to Angel Di Maria, and today, sometimes the ground was dry, and he gave us air each time he got the ball."
Argentina, who will face Netherlands or Costa Rica in their semi-final on Wednesday, seemed happy to hand the initiative to Belgium after their early breakthrough.
"I'm very happy for the players who played an excellent game, I'm very happy for them and the Argentines who have waited 24 years for us to be among the best four in the world," said Sabella.
"But we have to conserve energy. We played extra time (against Switzerland) and four games in a row at midday, so we will see how we recover and then we'll look at the team."
Messi said it was an unusual match for him.
"We played really well, especially in defence, they almost didn't hurt us. I think this was one of the best matches for us," he told reporters in the stadium.
"It was a odd match for me. I had to go back, run, go up and down and try to stop their players, but we showed solidarity.
"We fulfilled our first dream, we're among the last four. We're so happy we broke the jinx and got to the semi-finals after so long. Maybe we didn't attack a lot but neither did they."
- Sports & Recreation
- Gonzalo Higuain