Things appeared to be going to plan for the reigning world champions as Xabi Alonso put them ahead with a penalty just before the half-hour mark, following good work by Diego Costa.
However, Robin van Persie levelled with an audacious header in the 44th minute and things only got worse for Spain.
Van Persie netted again after the break, while an Arjen Robben double and Stefan de Vrij effort completed the humiliation as Louis van Gaal's men were rampant.
In the wake of the defeat, Alba suggested that the team's tiredness may have contributed, but he claimed that was not an acceptable excuse for such a 'shocking' loss.
He said: "We are physically quite fit. All teams got to this World Cup in the same condition.
"It's the end of the season, it's true we might not be at our best in this sense, but that's not an excuse. We are all at the same level.
"So the coaches are working well on this as they have always done in the previous years. What happened yesterday was an accident.
"We conceded silly goals that we normally haven't conceded in the past. It was a surprise for us as in the last two major tournaments we conceded two and one goal tops per game.
"So it is quite shocking we conceded five in our first one. Anyway, we have to keep working in this sense and I'm convinced we'll move forward."
