Pardew - formerly in charge at St Mary's - was subjected to "you're getting sacked in the morning" chants from both sets of fans toward the end of the contest.
However, the 53-year-old challenged his troops to "tough it out" and hopes that United can show their true quality next time around.
"We didn't have long to prepare after the internationals but there's no excuse really. The players tried everything at 2-0. We just caught at the start," he told BBC Sport.
"The criticisms from the fans are fair. You can't get beat 4-0 - I've had a few of those at the club.
"We have to be strong and tough it out. We have to put ourselves on the line and be brave. We have more quality than we showed today."
At 2-0, Newcastle fans also took to Twitter to vent their frustrations and started a #PardewOut campaign against their beleaguered manager.