The visitors were shocked by an exuberant Red Star, who scored a quick-fire double through Milan Pavkov in the first-half.
And speaking after the game, Lallana said the players will want to bounce back quickly from the defeat.
"As players we've got to take responsibility. It was a slow start all round really, and we gave them far too many opportunities - especially from set-pieces," the No.20 told Liverpoolfc.com.
"We had chances and we came out at the start of the second half which was better, but we weren't ruthless enough and we weren't patient enough.
"They time-wasted and we lost momentum but to come in 2-0 down wasn't like us and we've got to take full responsibility and make sure that doesn't happen again. It's still in our hands and if we win our next two games we go through, but it was a great opportunity missed for us.
"Of course there will be a reaction. It's not the first time we've lost games and it's about how you react and how you bounce back but we are thoroughly disappointed to come away with nothing."