The Reds lost the final 3-1 to the La Liga club at St. Jakob-Park on Wednesday.
Belgian keeper Mignolet also revealed manager Jurgen Klopp's reaction following the disappointing result.
"Straight after the game he called the lads together and said 'especially the second half, we can learn from these things'," Mignolet told Liverpoolfc.com.
"It's not easy straight after the game because everybody is disappointed, you feel that.
"You're looking for the answers, but you can't really find it at this moment in time. The thing is that we have to learn from this and get stronger for it.
"We're still a young group of lads and we'll get better from this.
"So short after the game you just feel so disappointed. You don't really know what comes with it.
"It's very difficult to be objective after this and you just feel the fact that you lost the final - that's the only thing you can describe at this moment.
"You're looking for the answers that you can't really find at this time."