Bayern are on the verge of their third Champions League final in four years after a brace by attacking midfielder Thomas Mueller and strikes from Mario Gomez and Dutch winger Arjen Robben floored Barca at Munich's Allianz Arena on Tuesday.
It was the Spanish giants worst Champions League defeat since the 1997 group stage 4-0 loss to Dynamo Kiev.
Barcelona's Argentinian superstar Lionel Messi started, despite struggling with a hamstring injury since the start of the month, but the world player of the year was a shadow of his usual self.
"They demonstrated they are stronger than us, they beat us in all departments," said Messi.
"I couldn't do much to alter the result, which was a shame.
"It will be hard at the Camp Nou, but we have to go for it."
Roura, though, accepted that his side faced a task which could prove even beyond them.
"Miracles are always hard to make real, 4-0 is a huge deficit to make up," he said.
"I don't know if anyone has come back from a score like that in the history of the Champions League, but we'll do what we can.
"This is a big defeat which hurts us a lot."
There were furious protests from the visitors when referee Robert Kispal failed to spot Mueller's body-check on Jordi Alba as Robben scored Bayern's third goal on 73 minutes, but defender Gerard Piqué said Barca were well beaten.
"They thrashed us," admitted the centre-back.
"The referee didn't have an influence.
"It is almost impossible for us, but we have to show some face in the return-leg.
"They were quicker, stronger and better."
Bayern, who are bidding to become the first German team to win the treble of European, league and cup titles in a single season, were buoyant after finding themselves on the verge of the Wembley final on May 25.
"That's crazy, hard to believe," said Robben.
"They've dominated Europe in the last few years and and then we go and win 4-0.
"The key was we fought and defended together."
But Bayern coach Jupp Heynckes warned the job is only half done.
"Of course, we're all very happy about the win, especially the size of the margin. We were first-class," he said.
"But we know we still have 90 minutes ahead of us in Spain.
"We want to enjoy tonight, but nothing more."
An exceptional day for Bayern got off to an unusual start when it was announced they had signed young German star Mario Goetze from arch-rivals Borussia Dortmund for a reported 37 million euros.
Then it was reported that in March club president Uli Hoeness, caught up in a tax evasion scandal, was arrested and released on bail after a police raid on his home, but he was at the Allianz Arena to witness an incredible night.