Milan were beaten 4-0 and went out 4-2 on aggregate.
"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," said Flamini.
"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.