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Los Colchoneros ran out winners thanks to second half strikes from Antoine Griezmann and Kevin Gameiro, as the Giallorossi missed out on the opportunity to book their place in the knockout stages of the Champions League with a game to spare.
"We played better in the first half, but we gave the ball away a bit too much after the break and that played into their hands," Fazio noted.
"It’s not the defence’s fault – we’ve been doing a good job. They came at us again and again but we stood firm, then they managed to score. I think we’ve done good work in defence and we need to keep that up."
He added: "They’re very good at pressing. They forced us into giving the ball away a bit and that was decisive."
The result means everything goes down to Roma's final match of the group stage, as they host Qarabag at the Stadio Olimpico.
A win guarantees Roma's spot in the last-16.
"It’s a must-win game," Fazio said. "Winning is the only thing that matters. The support of the fans will make it easier for us."
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