The Seagulls claimed the scalp of the Magpies for the second season in succession, recording a deserved 2-0 victory in their third round clash at the Amex Stadium courtesy of goals from Andrea Orlandi and Will Hoskins.
Pardew, who was missing a host of first-team players through injury, made five changes to his starting XI and saw captain Shola Ameobi harshly dismissed for two second-half bookings.
The North East club, who finished fifth in the top-flight last term, are just two points above the drop zone and have lost 11 of their last 14 matches in all competitions.
Speaking after the match, Pardew said: "We are missing too many of our top players. The season we're having we just need to get our best players back.
"We need to sustain ourselves in that and make sure we are a Premier League team next season.
"That team (against Brighton) is a shadow of the team we can put out."
Pardew hinted he might make further moves in the transfer window to strengthen his injury-hit squad, with defender Mathieu Debuchy having joined, while Demba Ba has departed for Chelsea.
He said: "We know we need to get some bigger players who can handle the situation of carrying a Newcastle jersey, whether that's a signing or getting a player back from injury."