The La Liga leaders thrashed the Serie A outfit 4-0 at Camp Nou on Tuesday night to progress to the quarter-finals and avenge their 2-0 defeat at the San Siro in the first leg of their last-16 tie.
Niang hit the post with the score at 1-0 on the night just moments before Lionel Messi doubled the Catalan club's lead, but Flamaini says that the 18-year-old should not be held responsible for their elimination.
"We can't put all the blame on Niang. If he had scored, it would've been a different game, but this is football and you only get one chance," Flamini said. "Barcelona had a great performance, showed all their quality and are among the best teams in the world.
"We tried to play, but it was so difficult for us today. Perhaps we were a little nervous at the start, as we gave the ball away many times and didn't play the way we usually do.
"Barcelona pressed high up the field and it was tough for us to emerge. They played very quick passing too and deserve to be complimented. There is bound to be a psychological blow-back after a game like this, which is difficult to forget. Now we have to put it behind us and stay concentrated on Serie A."