Alcacer has hit seven goals in four matches for Dortmund since joining on loan from Barcelona, where he struggled to break into the team and was rarely picked by Enrique during his time in charge at the Camp Nou.
Enrique might be having a change of heart after this predatory display from Alcacer on an emotional night for Spain, who stood before kick-off for a minute's silence in memory of the victims of the Majorca flooding which has killed 12 people.
But Enrique has won all three of his games since taking charge after the World Cup and this emphatic success was the ideal preparation for Spain before they resume their Nations League campaign against England in Seville on Monday.
"It was an intense game. I loved my team's attitude. They did what I wanted them to do," Enrique said.
"The disappointment for me was in the basics. If you don't do the basics against a very good team, you're in trouble," Giggs said.
"There were so many mistakes. Spain are such a good technical team, but we gave away two poor goals at set-pieces.
"After that you are chasing shadows. We got taught a lesson in many aspects." This was the first meeting between the countries since 1985 when Wales enjoyed a famous victory in a World Cup qualifier.
To mark the occasion, the match was held at the Principality Stadium, which traditionally serves as the home of Welsh rugby, for the first Wales football fixture there since 2011.
- Speed and precision -
Yet it took just eight minutes for Spain to silence over 50,000 Welsh fans. When Wales goalkeeper Wayne Hennessey punched clear to the edge of the area, Jose Gaya quickly worked back it back to Alcacer and he rifled a fine finish into the roof of the net.
Moving the ball around with speed and precision, Enrique's team doubled their lead in the 19th minute.
After all their slick approach play, Spain's second goal was actually a prosaic affair as poor marking from Suso's free-kick left Ramos unmarked to loop his header past Hennessey.
Once again it was Alcacer who did the damage for Spain's second in the 29th minute, punishing more sloppy Wales defending as the hosts twice failed to clear before the forward fired home.
Bartra made it four in the 74th minute as the substitute guided his header past the flat-footed Hennessey.
Vokes headed home with seconds left, but it was too late to salvage a dispiriting night for Giggs and company.
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