Mohamed Salah’s brace and other strikes from Roberto Firmino and Sadio Mane condemned Roy Hodgson’s men to their 13th league defeat this season despite efforts from Andros Townsend, James Tomkins and Max Meyer.
The loss left Palace only three points above the relegation zone and the Cote d'Ivoire international who contributed an assist in the tie has charged his side to improve at the rearguard.
"You can't come to Anfield and score three goals but still lose," Zaha told club website.
“We need to tighten up because some of the goals we conceded are just not good enough, so it's not a case of we performed well but were unlucky, we just need to be better, a lot better.
"Yes I am happy with the assist but it makes no difference if you lose the game so even though I am happy to have provided the cross and obviously pleased Andros [Townsend] managed to score, at the end of the day we lost and we need to put it behind us now."
"Any game I play in is one that we all want to win and the game against Tottenham will be no different, so after this performance [at Liverpool], even though we are not happy we lost, we will take the positives and hopefully get a win next weekend."