A double change when the players returned for the second period saw Joe Bradshaw and Mor Talla Ndiaye introduced for Liverpool.
But their hopes of mounting a comeback were reduced within a minute of the restart. Walker-Smith found space from a corner and glanced in a header for 3-1.
The Reds might have struck back during a positive subsequent spell, with two chances created by the intelligent crossing of Morrison on the right.
Josh Sonni-Lambie clipped a first-time volley just off target and then Will Wright stretched well at the back post to send the ball at goal, only for Lee to block.
Pecsi gloved away a 20-yard drive by Whyte and appeared to get fingertips on a deflected Matteo Dashi rasp from the edge of the area.
The Liverpool goalkeeper’s impressive efforts continued as he reacted quickly to claw away Ben Casey’s low curler after he stole the ball from Calvin Ramsay.
But Palace’s pressure told in the closing stages, adding two more goals to their tally.
Their fourth came from the penalty spot, Kyle Kelly having brought down Joseph Gibbard. Up stepped Rodney to fire into the top left corner despite a Pecsi touch.
Umolu made it 5-1, dispatching a rebound when Casey – having been fed through from deep – was the latest to be thwarted by Pecsi.
Team
Liverpool: Pecsi, Ramsay, Pinnington (Ndiaye, 46), Nallo, Pitt, Kelly (Laffey, 80), Morrison, Pilling, W. Wright, Sonni-Lambie (Ahmed, 80), Onanuga (Bradshaw, 46).
Unused sub: Misciur.
Next up
Liverpool will now await confirmation of their opponents in the end-of-season play-offs, with the regular campaign across the league to finish on April 17.