It was Barcelona's heaviest European defeat since 1997, when they lost by the same result to Dynamo Kiev, and it means they now need a football miracle in the second leg at the Camp Nou on May 1 if they are to reach their third continental final in five seasons.
Never in the tournament's history has a 4-0 deficit been reversed in a second leg.
The headline of Mundo Deportivo was "Catastrophe in Munich!", while Marca opted for "A Scandalous Defeat!".
Barca defender Gerard Piqué was honest enough to admit: "They are stronger and faster than us, and play football better. They have given us a real thrashing."
Piqué added that the tie was "now almost impossible. But we will have to give it everything in the second leg and try to win for our fans."
Unlike several of his teammates and large sections of the media, Piqué refused to criticise Hungary's referee Viktor Kassai, saying: "The referee did not have influence in the result. They were superior. That is all."
However, Mundo Deportivo labelled Kassai's handling of the game "calamitous" and claimed that Bayern's first three goals "should have been disallowed", either for fouls or offside.
Penalties for Bayern
On the other hand, the Catalan sports paper did accept that Bayern should have been awarded two penalties.
Radio station RAC-1 pointed out that Barca have had dubious goals given against them in all three of their knockout away games, at Bayern, Paris Saint-Germain and AC Milan.
Meanwhile, Barcelona assistant coach Jordi Roura said: "Bayern have to be congratulated. They were very strong; they are a very physical team. We didn't play all that badly in the first half but then they scored quite early in the second from a strategic move and from there it was difficult.
"Bayern played a great game while we were lacking that freshness to compete with them and that is something that we have to look at. We didn't see situations where we could have changed things after the break. We know that the situation is difficult but as Barcelona we have to compete in the second leg and try to win. We will give it our all."
Roura and head coach Tito Vilanova were criticised for only making one substitution, bringing on striker David Villa with just eight minutes left.
The Spanish media agreed that Barca's two problems in Munich were the poor physical condition of player Lionel Messi – just back after two weeks out with a strained hamstring – and some appalling defending.
Radio Marca claimed that it was "one of Messi's poorest ever performances", whilst AS called him "a shadow of his usual self".
Dejected Messi
A dejected Messi said: "They were superior physically, they won all the 50-50 balls."
Regarding his own physical state, he pointed out: "This was the first time I played since my injury, but I felt strong enough to play."
Messi finished by saying "it will be difficult to turn around a 4-0, but we will certainly try".
An online poll taken by Mundo Deportivo showed that only 19% of readers think Barca can now save the tie.
Youngster Marc Barta has been slated for a shaky display, though most papers pointed out that Vilanova had to cobble together a makeshift defence because of injury to veterans Carles Puyol and Javier Mascherano. Barta wasted the only two goal chances that Barca created all match.
'Physically than us'
In addition, left-back Jordi Alba will be suspended for the second leg.
Veteran playmaker Xavier "Xavi" Hernández i Creus said: "We are sad but we have to recognise that they were superior. Perhaps the result is a little exaggerated, but they were superior. We have to congratulate them."
"Our possession [64%] was sterile. We suffered a lot with their corners, they are better physically than us … We have to try to turn this round out of pride, we have to try to pull off a miracle, though we know it is practically impossible."
Right-back Dani Alves said: "They competed better than us, especially in the air. They were stronger and had a better rhythm. We have to congratulate them for this. But there are still 90 minutes left and we can make them suffer." – Sapa-dpa