Palace have enjoyed some memorable success over Liverpool during recent encounters at Selhurst Park and history looked set to be repeating itself when Fraizer Campbell scored a 15th-minute opener.
But Brendan Rodgers' men proceeded to dominate long periods of the contest thereafter and, although Palace held onto their lead until half-time, goals from Daniel Sturridge and Adam Lallana after the break secured a quarter-final berth for the visitors.
"We probably didn't have enough moments," Pardew told BT Sport.
"I felt we didn't put enough pressure on Liverpool and we really had a great chance at half-time.
"We know inside that dressing room that we should have done a bit better.
"Liverpool's system is a problem at times - they can keep the ball, they've got lots of options.
"Having said that, I was disappointed in the first half. The goal kind of made us a bit negative.
"We got it so early and we kind of sat back a little bit too much."
Pardew, who has presided over five wins in eight matches since taking charge of a club he represented as a player, also paid tribute to Liverpool's quality throughout the match, but reflected ruefully on a wasted chance when the score was 1-0.
"They're a tough team with technical players who ask questions," he added.
"It's a great first goal, almost unstoppable to a degree - great pass, great finish.
"Maybe the pivotal moment was in the first half when Dwight Gayle had a one-on-one. If he'd put that in we'd have been very difficult to beat."
