Liverpool lost 2-1 to Danish side Brondby in their first pre-season game.
Manager Brendan Rodgers made up for the absence of his World Cup contingent by using his entire travelling squad in the match but saw the Reds go in 1-0 behind at half-time following Christian Norgaard's fine finish past Brad Jones.
Swedish teenager Kristoffer Peterson levelled within five minutes of the restart but Liverpool were beaten deep in injury-time when Ferhan Hasani broke clear.
Crystal Palace had it easier in a one-sided run-out at Austrian side GAK Graz.
They breezed to a 13-1 victory, Stephen Dobbie netting four times in the second half while Glenn Murray, Joe Ledley and Jonathan Williams each notched twice.
Yannick Bolasie, Jerome Thomas and Marouane Chamakh rounded off the rout.