Valverde’s side won the first leg of last year’s quarter-final 4-1 in Spain before a 3-0 defeat in Rome knocked them out on away goals.
Although Liverpool would need to score four goals in order to win in normal time, a repeat of that result would force extra-time and maybe penalties.
“Last year we went in the quarter-finals with three goals [against Roma] and they came back to us. The tie is open, there is no reason to trust us,” Valverde claimed.
Liverpool lost 3-0 at the Nou Camp on Wednesday evening, with Lionel Messi’s late free-kick putting Jurgen Klopp’s Reds in a difficult position.
Valverde is keen to add the Champions League to their La Liga title this season, but he remains adamant that the tie is not over.
“Sometimes you can dominate the pace of the game and other times the game dominates you,” he added.
“Sometimes we tried to put a pause, but they then pushed us back. And we were interested in going forward, not back.
“If they do not score in your home, it’s a great result.
“It is clear that they have pressed us and that we have suffered to keep a clean sheet, but it is also true that we have managed to do so.
“The match has been matched, there have been minutes in which they have been better and minutes in which we have been better.
“They have the capacity to make us suffer, us and anyone.”
Virgil van Dijk has urged his team-mates to come together in their pursuit to end the season with a trophy.
He said: “They still have that extra quality but we will try to do everything possible to go through.
“But it is 3-0 and we have a big job to do at Anfield but we have shown throughout the season that we never give up. We need everyone to be together and let’s see how it goes.
“The only thing is that we can only keep believing and keep working hard for each other and stay positive and there is no reason to panic.”