Alexis Sanchez and Jorge Valdivia struck in the opening 14 minutes and the South Americans held off a fightback from Australia before sealing a 3-1 win at the FIFA World Cup on Friday.
Sampaoli called on a 'more complete' performance from his team when they face Spain and the Netherlands in Group B.
"It was important to win because it was a difficult game," he said.
"We kept going because it is important to win the first game if we are to have any type of aspirations to do well.
"But to take on our other rivals, we must make our matches more complete."
Sampaoli was pleased with his team's opening half-hour, only for them to concede to a Tim Cahill header in the 35th minute and have to hold firm before Jean Beausejour's late sealer.
"The pressure that we put on in the first 30 minutes was good, we managed to subdue our opponents. Australia were able to overcome that, but I have a happy dressing room," Sampaoli said.
"There are things that we can do better, this isn’t us at our best.
"The players gave their all for the shirt and were very professional."
It left Chile second in the group after the Netherlands crushed reigning world and European champions Spain 5-1 earlier on Friday.
Sampaoli warned his side it would still be tough when they face Spain on Wednesday.
"Spain are the world champions, we know that they have suffered a blow but they are one of the best teams on the planet," he said.
"It doesn’t matter who the next opponents are, the key is to keep on playing good football."
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