Dominik Szoboszlai struck an 88th minute winning penalty, earned by Florian Wirtz - and confirmed by VAR - to secure an important three points.
Afterwards, a disappointed Chivu stated: "A draw was fair given the way things were going. We were initially under pressure, but then we found the key and the right moves.
"Then we made two substitutions that affected us at the key moment; we were forced not to make them. Then came an incident at the end of the match, the second in the last two Champions League matchdays, and we didn't take anything home.
"We tried to give our best, we we had the courage to go all the way. We should have been more focused going forward; it was a match affected by the two substitutions."
On the penalty, Chivu continued: "I rarely comment on refereeing decisions; I talk about manners and what we need to teach. The referee interpreted it well during the match, but when VAR intervenes, you have to understand the dynamics.
"We have to accept the referee's decision, we have to fight against injustice and think about what good we want to do."
On Liverpool, the Romanian concluded: "We expected their pressure, their intensity. We started a bit intimidated. We found some ways to play, and in the second half we expected to continue that energy, and we tried to do so. But when the energy dropped, we let ourselves go a bit too much."