Patrick Cutrone scored three minutes into the second half to give the Rossoneri the advantage - a moment that Fazio thought changed the course of the game, considering Milan had not created a clear-cut opportunity prior to that.
Davide Calabria scored with 15 minutes remaining to confirm the result.
"I think we did well in the first half today; we moved the ball about nicely, but we lacked a cutting edge in front of goal," Fazio said.
"They scored from their first chance and that knocked the team. The match got difficult after the opening goal. We must look forward and keep on fighting right until the end.
"We have a very important match next week, one where we need real self-belief if we want to win."
The Giallorossi now face important league meetings against Napoli and Torino, before Shakhtar Donetsk come to Rome for the second leg of the Champions League last-16 tie.
“If we think that we are in a bad spell things won’t get better," he said. "We have to believe in ourselves, be positive, work hard and battle right up until the final game.
"We have to work hard; I know the ability of this squad and we are focused on finishing in third spot.”
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