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.
Nigel Pearson's Leicester side earned plenty of plaudits for the way they dismantled United's frail defence to come from two goals behind, but Moore reckons securing points on off-days is just as important in the Barclays Premier League.
"After such a good result last week you always want to build on that and we didn't," the defender 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 and it is always going to be hard to get back from there.
"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, we got a lot of praise for the way we played against Man United but it is days like this that we need to get something from."
Despite good results against Arsenal and Everton, it was the win over United which saw Leicester become headline makers but Moore insists the players did not let that go to their heads.
"We have all worked very hard in training, like any other week.
"We just haven't got the result we wanted and they were bad set-pieces to concede from but that is what has happened and we just need to forget about it.
"We have dealt with it (the spotlight) very well
We were confident coming into the season and have picked up a good amount of points, we really wanted to build on that but it didn't happen."
Leicester will be looking to bounce back when they host fellow top-flight newcomers Burnley at the King Power Stadium next weekend.
The Foxes finished nine points clear of Shaun Dyche's side last season as both gained automatic promotion from the Sky Bet Championship.
That form has carried over into the current campaign as Leicester have so far amassed eight points, five more than the Clarets and Moore is not expecting a hangover from the Palace defeat.
"We have a strong team ethic," he added.
"It is something that the management staff drill into us, they say we can't get too high or too low
We will probably pick out a few bad points from the performances on Monday and then it is out of the window and we move on because the Premier League is ruthless and you can't dwell on anything too much."
Palace have now picked up eight points since Neil Warnock was appointed as Tony Pulis' successor last month - and this was their first league win in front of their own fans this season.
Record signing James McArthur has slotted straight into the midfield alongside Joe Ledley and Jedinak and felt the win over Leicester was important after beating Everton and with a tough run of games on the horizon.
"It is massive," he said of the win.
"We know we are going to have a tough run coming up against the so-called bigger teams and to get that winning mentality going into those games is brilliant.
"To get three points after Leicester getting a big win last week it was momentous really
We worked hard to get it.
"We knew it was going to be tough today and they caused us problems now and then and we called upon our goalkeeper to make a great save and then sneaked in-front before quickly adding a second."
Source : PA
Source: PA