Pedro struck late for the 2-1 Champions League win.
“It was the kind of game we predicted, high intensity, as Celtic are not an Anglo-Saxon team, they have technique, speed and dynamism," Sarri told Sky Italia.
“I think we had a great first half and had the opportunity to take the lead, then we had a period of being under pressure, but this time we showed more character to stay in the game. When that happens, usually you are rewarded.
“I told the lads before the match that we were nearly there, not to listen to what anyone else says. We are close to being competitive, but that 'close' is the difference between winning or not. It is a gap that can be covered and I hope this result can give us a positive reaction, some confidence and belief.
“It is a midfield that has good characteristics, but playing every three days, we need to have other solutions too. On the winning goal at the 96th minute we had Taty Castellanos, Guendouzi and Pedro involved, all substitutes. We are making far more changes both from one game to the next and during the match compared to last season.
“Playing with this calendar and this tempo, some players are struggling at the 60th minute, especially after playing regularly in recent games. I also wanted to preserve them for the next match."