Ghanaians Kevin-Prince Boateng and Sulley Muntari scored one apiece in a lively second half as the hosts, impressive defensively throughout, stunned the Catalans in their last 16, first leg, at the San Siro.
Roura, standing in for Tito Vilanova while the coach undergoes cancer treatment in New York, admitted the Primera Liga leaders had simply not done enough.
But the 45-year-old Spaniard, whose top flight playing career was all but ended at the San Siro in 1989 after suffering a serious knee injury while playing for Barcelona, also claimed the pitch was unfit for a Champions League game.
"It's bad to lose 2-0 but we're convinced that when we'll be playing at home in front of our own fans on a pitch that is fit for this competition, we will overcome this setback," said Roura.
However, the stand-in coach refused to write off his side's chances of making the quarter-finals just yet.
"We had the game under control, although admittedly we didn't create too many clear chances and neither did they," he said.
"We hoped we could wear them down. Their first goal was an isolated attack following a shot and a rebound.
"It's a bad result but I'm absolutely convinced that we can turn this around in the second leg with the support of our crowd."
Milan had started the game brightly, with Muntari flashed an early shot over the bar from long range for Milan.
Philippe Mexes made a vital clearance at the other end to prevent Jordi Alba's cross reaching Pedro Rodriguez and though the same defender then handled Dani Alves' delivery, Pedro had already been flagged offside.
Stephane El Shaarawy's poor touch saw a good chance slip away but resulted in a corner, taken by the prolific young striker, from which Boateng shot just wide.
Christian Abbiati held Xavi's well-struck 30-yard drive and El Shaarawy tracked superbly to the left-back position to break up another Barcelona attack.
Mexes collected the first yellow card for tripping Lionel Messi and as Barca pressed, Riccardo Montolivo prevented Pedro's back-heel reaching Cesc Fabregas.
Boateng's cross eluded a sliding El Shaarawy before a goalless half petered out somewhat.
Sergio Busquets was booked early in the second period after fouling Giampaolo Pazzini, moments before the controversial opening goal.
Montolivo's shot took two deflections, the second off the raised arm of Cristian Zapata, before Boateng fired low past Victor Valdes. Gerard Piqué was booked for protesting to Scottish referee Craig Thomson.
Messi blazed an uncharacteristically wayward free kick high into the stand before Andres Iniesta almost charged down Abbiati's clearance in the six-yard box.
Valdes saved Pazzini's acrobatic volley but at the other end, Iniesta fizzed a drive a foot or so wide and Xavi curled a free kick just over.
But it was Milan who found a second goal with nine minutes remaining as substitute M'Baye Niang and El Shaarawy combined to set up Muntari, who gave their beautiful approach play the classy finish it deserved.
Massimiliano Allegri, the Milan coach, was pleased by his side's performance.
"The boys deserved this result," he said afterwards.
"They didn't give anything away at a defensive level and they made the most of the we had.
"We could have perhaps done better with the chances we had in the first half, and finished the game with a third goal, but we never believed we would be going to the Nou Camp with a 2-0 advantage."
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