Alves praised the performance of the Italian side and also urged his teammates to improve if Barca are to reach the quarter-finals.
"We have to be better competitors," Alves told the club's official website. "We didn't play a good game, we didn't create goalscoring chances and that's what you have to do to win.
"It's not that we played terribly after the first goal. We didn't play well in general and that's largely due to how well our rival played. We have to improve.
"This is a difficult result. We have to fight back, go for the [return] game and work hard."
Alves has played in five of Barca's seven Champions League games so far this season.