Dries Mertens missed an early spot-kick for Napoli and they fell behind just before the hour-mark against Udinese in their Coppa Italia last 16 clash.
Jorginho levelled from the penalty spot before Udinese had Silvan Widmer sent off for a second yellow card.
Udinese still forced extra time though, and even after Marek Hamsik gave Napoli a 99th-minute lead, they still responded - this time through Panagiotis Kone.
That took the clash to penalties but defending champions Napoli held their nerve to set up a quarter-final with Inter.
"When we went 2-1 it up it seemed over," Benitez told RAI Sport.
"But Udinese scored again and we need to defend better in these situations.
"I had faith we could do it, as the team was in control.
"We were missing the final ball and Udinese were only occasionally dangerous."
Benitez reserved special praise for Slovakian Hamsik and hopes he can kick on from the performance.
"He had some good performances recently and this goal will really boost his confidence," Benitez added.
"We know he can make the difference and he is hugely talented, so I hope the goal increases his self-belief."
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