Samba missed the clash through suspension while Nelsen was ruled out with a thigh injury as Reds duo Sotirios Kyrgiakos and Fernando Torres found the net either side of Jamie Carragher`s own goal.
Allardyce said: "In the end we could not hold on any longer because we did a sterling job trying to hang on in the first half, particularly Paul Robinson.
"We could not cope with the aerial side of Liverpool because of the loss of Chris and Ryan, who are dominant in those areas, and we eventually cracked.
"We got an opportunity to do better when we scored but when I see the second goal it is the reason why we missed those central defenders. We wouldn't have let Fernando Torres in there free, six yards out, had we had Samba and Nelsen. But I can't complain about the result."
Source: PA
Source: PA