Juve's elimination followed five defeats in six Serie A matches and December's exit from the Champions League group stage.
Media reports have said a caretaker could now be appointed until the end of the season with ex-Juve defender and Italy under-21 coach Claudio Gentile among the favourites.
"I have received no communication so tomorrow it's training," a dignified Ferrara told Rai television.
His team's woeful run continued despite taking a 10th-minute lead when Inter reserve goalkeeper Francesco Toldo let a Diego shot through his body.
Hosts Inter deservedly equalised when Lucio prodded in Wesley Sneijder's deflected free-kick midway through the second half and forward Balotelli sealed victory after Gianluigi Buffon could only parry Thiago Motta's shot.
Juve fans were banned from the San Siro for their racist chants against Balotelli in recent months.
Giorgio Chiellini did hit the post for Juve while they were leading but Inter had more chances and were furious not to be awarded a penalty when Felipe Melo handled Thiago Motta's flick just before the break.
"We didn't ask for a penalty, football did," said Inter coach Jose Mourinho, already angry with the refereeing in Sunday's 2-0 win over AC Milan when he had two men sent off.
"It's best to forget what happened at the end of the first half because if we don't, I don't know what to do."
Mourinho, who said his side clearly deserved to win, had sympathy for Ferrara given media reports have linked a host of coaches to his job including Guus Hiddink and Rafael Benitez.
"He deserves respect. Talk about replacements after he is sacked but not before," said the Portuguese.
The Italian champions will meet Fiorentina in next month's two-legged semi-finals with the other tie between AS Roma and Udinese, who beat Milan 1-0 away in Wednesday's quarter-final.
