A comfortable afternoon saw Palace sweep aside their non-league hosts in the third round, courtesy of a first-half double from Scott Dann, as well as strikes from Dwight Gayle and Kevin Doyle.
Pardew was delighted with what he saw from his new team, having taken his place in the dugout for the first time since his arrival from Newcastle United was confirmed on Saturday.
He told BBC Sport: "We applied ourselves well today, we ticked all the attitude boxes you want to tick.
"We needed to show a bit of exuberance and a bit of class and the players used that instruction really well.
"We never looked in trouble really and at any level that is very difficult to achieve."
Pardew joins Palace on a mission to help them retain their Premier League status, and he is in no doubt about the potential of his new squad.
"We have really good honest players. Their attitude, even before I arrived, was spot on. We just need to open our wings a bit and show we can play.
"I know the heartbeat of the team, I know how it works. The chairman and I are looking to improve things on all levels but the honesty of the players will hopefully see us through.
"This is Crystal Palace's day and I am pleased for the club. The fans showed one of the reasons why I have come here because their support today was phenomenal."
Meanwhile, Palace's two-goal hero Dann told BT Sport after the game that he was confident Pardew's arrival would help to kick-start the club's season.
He said: "The new manager coming in has given us a good boost and it was an opportunity for some of the lads to come in and show us what they've got.
"He [Pardew] has come from a top club and we're delighted to have him on board. Hopefully we can keep putting in performances like that in the Premier League."