The Foxes travelled to Selhurst Park on the back of a famous 5-3 victory against Manchester United but could not reach those heights as two goals in three second-half minutes secured a first home win of the season for the hosts.
Fraizer Campbell and Mile Jedinak both converted from set-pieces to secure a 2-0 victory and their own back-to-back wins after triumphing at Everton last week.
“After such a good result last week you always want to build on that and we didn’t,” Moore said..
“Whatever division you play in, and any league in the world actually, if you concede two goals from set-pieces it is going to be disappointing.
“Both teams were a bit too cautious at times and it did not look like pretty football but it is all about trying to grind results out which Crystal Palace did.
“Maybe we need to learn how to win ugly.”
CRYSTAL PALACE: Speroni, Kelly, Dann, Delaney, Ward, McArthur, Jedinak, Ledley, Puncheon, Campbell (Chamakh 73), Bolasie (Guedioura 90).
LEICESTER: Schmeichel, De Laet (Simpson 64), Morgan, Moore, Konchesky, Hammond (James 71), Cambiasso (Mahrez 64), Drinkwater, Vardy, Ulloa, Nugent.
Referee: Keith Stroud (Hampshire).