Three Serie A games without a win and the club being up for sale had already set tongues wagging that Ranieri's future at Roma was in jeopardy, and the uninspiring display in the last-16 first leg has only raised the pressure.
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Flatly asked if he would resign after the multiple defeats, Ranieri responded with a dry: "No, I'm not even thinking of it."
He put on a brave face over his side's performance, denying last season's Italian runners-up were in serious trouble.
"We're not in a crisis, I didn't see a team in crisis today," he said at a news conference where he faced testy questions from reporters.
"A little bit of fragility maybe yes, we shouldn't have reacted in the impetuous manner we did when we were at 1-1."
Roma took the lead in the 28th minute when midfielder Simone Perrotta headed in a cross from Rodrigo Taddei off Razvan Rat, but fans had little time to savour the goal as Shakhtar equalised a minute later through Jadson's fortunate deflection.
Luiz Adriano slotted in the visitors' third before half-time, capitalising on a slip-up by Roma defender John Arne Riise that summed up their frustrating evening.
"I think we played a great game. We lost but I have nothing to reproach the boys for," Ranieri said. "I saw a team that never gave up. There are games that don't go well."
"I take all the responsibility for the boos, I feel really bad about that," Ranieri said. "The insults and the boos, I take them upon myself - the boys played a great game."
The coach's troubles come as American consortium Di Benedetto starts a 30-day period this week for exclusive talks to buy the cash-strapped club, which has spurred Italian media reports that Ranieri's job could be at risk.
Shakhtar coach Mircea Lucescu also paid tribute to Roma, but added that his opponents' weakness lay in their inconsistency.
"I'm convinced that Roma are unpredictable, they can play several great games in a row and they can lose," he said.
The Ukrainian league's winter break from November to March 5 means Shakhtar had not played an official match since Dec. 8, but the side showed virtually no sign of being rusty when they took to the field on Wednesday.
