Isco struck a hat-trick in a 6-1 demolition of the Lionel Messi-less visitors at Atletico Madrid's Wanda Metropolitano home, with Diego Costa, Thiago Alcantara and Iago Aspas also on target.
Spain coach Julen Lopetegui cautioned after extending his unbeaten run in charge to 18 matches that a friendly victory means nothing for his side's World Cup hopes.
And Barcelona coach Valverde agrees with Lopetegui, noting over-confidence could be a problem for 2010 winners Spain after they dismissed Argentina so easily.
"We can think that we will win it all," said Valverde. "6-1 is a wide margin, but that's all.
"It's dangerous because it can make you think that you have more points than you have before you start.
"[Argentina] lost a friendly game, but that doesn't mean anything. The World Cup has not started. There's nothing won by Spain or lost by Argentina."
Barcelona's Gerard Pique appeared to be struggling with injury before being replaced in the second half, while the centre-back was whistled throughout by Spain supporters.
Valverde did not expand too much upon his defender's injury and though he claimed not to hear what the supporters did to Pique, he believes the defender can handle it.
4 - Only David Silva (5) has assited more goals for Spanish national team than Iago Aspas (4) under Julen Lopetegui. Motivated. pic.twitter.com/1lwu9JIUJv— OptaJose (@OptaJose) March 28, 2018
"When he touched his knee I thought he had hurt it, as everyone did," Valverde said.
"I won't go into it [the whistling] because I usually watch it without the volume on, but I think he's dealing with it well."