The defending champions reached the last eight after winning all three group matches before overcoming Cape Verde and Egypt in two hard-fought knockout games. Argentina are now unbeaten in 11 World Cup matches and are chasing a second consecutive world title, something no nation has achieved since Brazil in 1962.
Despite their impressive run, Scaloni expects another difficult challenge against a disciplined Switzerland side.
Speaking ahead of the match at Arrowhead Stadium, the Argentina coach said he hopes his players leave a lasting legacy through their fighting spirit.
"I would like this national team to be remembered as a team that never gave up," said Scaloni.
He revealed he was moved after watching a young supporter passionately backing Argentina, saying moments like that remind everyone involved why they play for the national team.
"We, the technical staff, the players, we play football for this," he said. "We do not play football just for a win."
"When you see a 10-year-old saying those things and talking with that passion, and everyone shouting 'Argentina', that is just so emotional. That is the legacy that I want."
The quarter-final also sees Lionel Messi return to the stadium where he scored a hat-trick in Argentina's opening 3-0 victory over Algeria earlier in the tournament.
The Inter Miami captain is level with France forward Kylian Mbappe on eight goals in the race for the Golden Boot. Messi has also become the highest goalscorer in World Cup history with 21 goals across his career.
Scaloni believes age will not stop the 39-year-old from remaining at the top of the game.
"At 39 years of age, some people might think he may not rise to the challenge, but I've said before that for as long as he wants, he will be the best," said Scaloni.
"I'm not saying that because I'm coaching him, but because I believe if he wants to, he will continue to be the best."
He added that watching Messi train every day still amazes those around him.
"Those of us who see him train today cannot even imagine what he was like when he was 23 years old at Barcelona with Pep Guardiola."
Scaloni also praised Switzerland, warning that their experience and organisation make them dangerous opponents.
"They have a long-standing history in World Cups," he said. "They are physically strong and have very experienced players, so it will be a tough opponent."
"We respect them very much. They eliminated Colombia, and Colombia had been playing very well during this World Cup."
The winners of Saturday's quarter-final will meet either England or Norway in the semi-finals.
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