The result at the Mapei Stadium leaves the Giallorossi with only the slimmest of hopes of qualifying for next season's Champions League.
Claudio Ranieri's side hit the woodwork multiple times - while Fazio himself had a goal ruled out late on - but could not find the breakthrough.
"We tried everything, up until the last minute," Fazio said.
"We will keep fighting until the end of the final game. After half-time today we created a lot of chances, but we just couldn't find the breakthrough. It's a shame, it's frustrating we couldn't score."
He added: "We will see the results elsewhere tomorrow, trying to remain positive. We will keep going."
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