Croatia is the 2018 World Cup runner-up, winning its group that included Argentina before beating Denmark, Russia and England on the way to the final.
"We have played against teams that have gone very far in the World Cup ... and we have risen to the challenge", added Asensio, who after his incredible performance against Croatia, will head into Real Madrid's clash with Athletic Bilbao brimming with confidence on Saturday.
Goals from Saul Niguez and Rodrigo gave the visitors the three points after Marcus Rashford opened the scoring for Gareth Southgate's men.
Ivan Santini and Ivan Perisic missed good early chances before Spain seized control 23 minutes in, as Saul headed the ball in off the turf after being picked out by Dani Carvajal's sublime cross.
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Spain were in dreamland two minutes later as Asensio cheekily lofted a shot from 20 yards that ricocheted off the crossbar, before deflecting in off goalkeeper Lovre Kalinic for the third goal.
What does it mean?
Playing in a small venue in Elche - a site that rarely gets to host Spanish national team games - should confer the hosts a more significant, more intimidating home-field advantage than the usual atmosphere of a pseudo-friendly game played in the larger, cavern-like stadiums.
His first goal was emphatic and he deserved his second effort to go straight in, rather than deflect off the back of the keeper.
The 2010 World Cup winners slightly edge Croatia in the head-to-head record with three wins from six outings, while there has been one draw.