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The start of the game was somewhat spoiled when a minute's silence to remember Diogo Jota was interrupted by shouting fans.
Once the game was underway, Liverpool immediately got going and only needed four minutes to open the scoring through Hugo Ekitike.
Their advantage was short-lived, though, as Jean-Philippe Mateta pulled back a quick equaliser from the penalty spot.
Mohamed Salah, Alexis Mac Allister and Harvey Elliott all missed before Justin Devenny buried the decisive spot-kick for the Eagles.
Express Sport rates the Liverpool players from today's game...
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Alisson Becker - 6
Made an excellent stop to deny Mateta from close range before being sent the wrong way from the penalty spot.
Room for improvement.
Justin Devenny scored the winning penalty to seal victory for Crystal Palace (Image: GETTY)
Curtis Jones - 5
Was relatively quiet, blending into the background for most of the game, but completed all of his passes.
Missed a golden chance to win the game for Liverpool in the closing stages before blazing his spot-kick over the crossbar.
Got lucky when he handled the ball in the closing stages without giving away a penalty before missing his spot-kick in the shoot-out.
Harvey Elliott - n/a
A late addition.