Eusebio Di Francesco's side lost 5-2 in the first leg of their semi-final tie, meaning they must replicate their 3-0 win over Barcelona in the quarter-final second leg if they are to progress to the final.
Liverpool were 5-0 up with 68 minutes played, with Mohamed Salah and Roberto Firmino scoring twice and Sadio Mane also on the scoresheet, as the visitors failed to deal with the Reds' quick-fire passes to the front three.
However, late goals from Edin Dzeko and Diego Perotti gave the visitors some hope ahead of the return fixture in the Italian capital, and De Rossi is refusing to give up.
"We have to hold on to what we did in the quarter-finals," he told Mediaset Premium. "That tells us it's not impossible and that we have a duty to try, for ourselves and, above all, the people who love Roma.
"The only difference is that, against Barcelona, I felt it was an unlucky game, with dubious incidents. We had a good first 20-25 minutes here, then we were less good at covering the space, but it's difficult to do that when they're much faster than you.
"It's not right to put conceding so many goals on the defence. We all played very aggressively, even though we had the feeling of being able to affect little in midfield because they often bypassed it. They constantly went for the long ball, from any area of the pitch.
"Today was a case of our blackout and their great quality. It won't be easy, but we have to start from here. It's not impossible and we know that."
De Rossi also praised the performance of Salah, his former team-mate having produced arguably his best performance of a spectacular season, with two goals and two assists.
"We know Salah well, we know he is a great player as well as a great person," he said. "He's improved his quality in the final third and he's becoming decisive, as we thought he would."