Jurgen Klopp's side suffered a 3-0 defeat at Camp Nou in the first leg of the last four tie, which left the Blaugrana on the brink of a final berth, but the second leg did not go according to plan.
The Reds staged a remarkable turnaround at Anfield in the return, winning 4-0 thanks to braces from Divock Origi and Georginio Wijnaldum.
Barcelona were knocked out of the continental tournament in humiliating fashion for the second successive year, having been beaten by Roma in similar circumstances at the quarter-final stage in 2017-18.
Pique, who started both legs against Liverpool, has confessed that the result left a mark on the Spanish champions which will take time to heal.
“It has been hard to get up emotionally because the days passed and you did not forget the defeat, it is a fall that will last over time,” he told El Pais.
“But we must take a step forward. It was a very difficult situation. The team sees that it is not going, you see that they are squeezing and that it is very recent last year.
“But we must not torture ourselves. Yes, that is one of our great defeats. But that's the sport, where sometimes you have to bite the dust.
“It was a nightmare and you have to assume it because it can happen again.
"But we must understand why it happened and help us in the future because we want to raise the Champions [League] again.”
Ernesto Valverde's side were unable to learn from their mistakes against Roma, having also surrendered a three-goal lead against the Italian giants the previous season.
Barca have failed to reach the Champions League final since 2015 and Pique believes the memory of the upset at Stadio Olimpico affected the players' mindset against the Reds.
He also praised Liverpool for employing their infamous high press to great effect, before acknowledging the influence of the Anfield crowd.
“When something like this happens, everything or almost everything has gone wrong,” he added.
“I think that on a mental level, some people were affected by what happened in Rome because we had it very recently.
“With the first goal, which was very fast, unconsciously you see the image of Rome.
“Then two more came very quickly and it looked too much like what happened a year ago. Surely it was a mental block, but football was also missing.
“And they pressed very high, very intense, Anfield also played his role, we were not able. Sometimes happens. It was a very hard day.”