Totti scored the winning goal in the fifth minute of injury time from the penalty spot, firing home after Kevin Strootman had been fouled inside the box.
For the fans at the Stadio Olimpico it was almost the perfect ending for the Giallorossi, although the 40-year-old admitted he was not completely cool ahead of the decisive moment.
Roma will now face Lazio in a two-legged semi-final, with Totti hopeful his side can prevail.
“Yes, we're into the last four and hopefully we'll make it through to the final," he said. "We're not thinking about the fact it's a derby – it's a semi-final like any other and we'll try to give a good account of ourselves.”
On the penalty itself, he added: "Yeah, I felt a lot of pressure. It was one of the penalty kicks I've felt the pressure most in my career. I hoped not to miss it - I had a lot of responsibility.
"If the game goes to extra-time I don't know what might happen, especially as four or five of us were suffering with cramping. The important thing to score that penalty was to be focused, have conviction, and be absolutely sure of what I was doing."
Totti brushed away any suggestions that the late penalty was a dubious decision - and paid tribute to the quality Cesena showed.
"It was clearly a penalty," he said. "[Kevin] Strootman got there before the keeper and he sent him tumbling. We showed great determination to come through and win it in the end – and winning was all that mattered today.
“That was no normal Serie B side we were up against. They were very well set up and they came at us showing no fear. But in the end we got the result we wanted.”
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