Marcus Thuram struck in injury-time for the Champions League victory.
Barella later said, "We could have done much better, we left so many chances to our opponents and in the Champions League you risk conceding like that... Well done to those who came on, with the right attitude, good anyway because it wasn't an easy match.
"It's a confidence boost, a difficult pitch and a healthy team. We take this victory and the incredible attitude from everyone. I repeat, we could have certainly done better but the character was there."
For their next clash with Juventus, Barella said: "Juventus is a strong team, they have done a lot on the market and have a new coach so maybe they need time. In Serie A however there are many strong teams, we just look at our path and that's it."