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."
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He was referring to the Giallorossi giving up three goals to the Ukrainians in quick succession that left them two down before halftime and unable to ever regain the momentum despite a superb strike by Jeremy Menez after the break.
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.
The Ukrainians, who looked fresh despite not having played a competitive match in more than two months, then seized control of the match with a lovely curling shot from just outside the area by Douglas Costa on 36 minutes.
FRUSTRATING EVENING
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."
A glum-faced Ranieri was forced to lead Roma players off the field both at halftime and at the end of the game to deafening boos and whistles from an angry crowd at the Stadio Olimpico.
"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.
The second leg takes place in Donetsk on March 8.
