"Resignation? Let's leave that sort of talk aside, the thought has never entered my mind," he told reporters after Wednesday's game.
"I think any sort of comment would be superfluous, whether it be technical or tactical. All I can do is apologise. It was a terrible performance from every point of view."
The defeat came three days after Roma squandered a three-goal lead in a 3-3 draw at Atalanta in Serie A and missed a chance to move back into the top four of the standings.
"I want to get inside the lads' heads and understand what is going on," said Di Francesco, whose team have suffered embarrassing league defeats to Bologna, SPAL and Udinese this season.
"A few games back people thought the squad had bounced back, and instead we collapsed again too easily," he said.
"The main thing is the mentality, that ability to keep battling away in games even when things are going wrong – to stay together when things are going badly, not having the wrong attitude during the game," he said.
"You lose and you win together. This is what hurts most right after this game."
(Writing by Brian Homewood; Editing by Amlan Chakraborty)
