Rickie Lambert gave the visitors an early lead with his first Liverpool goal but the lack of confidence in Brendan Rodgers' team was all too evident as Palace battled back to win.
Midfielder Lallana told liverpoolfc.com: "It was disappointing, especially after going in front so early. It was a great platform for us to push on and control the game.
"But we didn't do that – we take full responsibility for that. We need to stick together. It's as simple as that. When you're having a tough time as a team, you all need to stay together – you can't start becoming individuals.
"We win and lose as a team; we need to stay together, keep fighting and keep working for each other. We have got a tough game on Wednesday so we all need to be together for that one.
"We need to win to stay in the competition, so the lads will be fighting for their lives to do that. It's important, not just for ourselves, but for the fans, the manager and everyone involved with Liverpool Football Club."
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