Barcelona had been overwhelming favourites to progress in the last-16 tie, but second-half goals from Kevin Prince Boateng and Sulley Muntari earned Milan a shock win at the San Siro.
Spanish league leaders Barcelona lacked their usual fluency in the first-leg encounter and struggled to test Milan keeper Christian Abbiati.
However, Roura is expecting a different game back at Camp Nou in three weeks' time and believes his side can still go through.
"We are confident in our own team and playing at our own stadium," said Roura.
"It will be a different story in the second leg. We fully believe we can turn this around.
"This wasn't our best game. Although we had problems I think that the result is excessive.
"They found a couple of opportunities and scored from them which now makes things tricky for us."