Verona won 1-0 thanks to a late goal from Diego Coppola with both teams in danger of relegation.
Cioffi said: "It seems like a paradox to me to talk about a defeat after such a performance, with so many clean opportunities created in the first and second half. An episode brought us to our knees, I didn't see this domination by Verona. A team should have won, this was Udinese.
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"By nature I'm a fighter and I never accept reality. These are hard blows to digest but there's no time to feel sorry for yourself, there's another match on Thursday to end with points.
"We were really sick against Milan in January, we conceded a goal against Inter and conceded a daring goal but tonight I didn't feel any fear. A dirty ball went under the crossbar, we weren't bad at closing it out."