The Hammers had gone 672 minutes without a goal until striker Marlon Harewood's fourth minute strike put the visitors ahead against Chesterfield, from the third tier of English football at Saltergate.
But Chesterfield fought their way back as the Londoners' attack ran out of ideas and were rewarded in the 54th minute when Colin Larkin equalised.
Caleb Folan's 20-yard shot was palmed onto the woodwork by West Ham keeper Rob Green and Larkin, following up, stabbed home the rebound.
And Folan grabbed the winner following a goalmouth scramble three minutes from time to condemn last season’s FA Cup finalists to their eighth straight defeat.
"It's where we are at the moment," said a frustrated Pardew.
"We put ourselves in the lead and at that point I felt we should have pushed on.
"But we never really got going, they wouldn't let us, fair play to them, I thought they deserved to win," Pardew added.
"These are players who produced great levels last year. But now, it's a different pressure," explained Pardew, whose side are second-from-bottom in the Premiership.
"We find ourselves out of this competition, out of the UEFA Cup and in a bad position in the league.
"We have to take that on board and face reality. It's a different challenge for the individual players. They have to step up to the plate and carry the burden of where we are.”
O'Neill's happy homecoming
Elsewhere, new Aston Villa manager Martin O'Neill, who won the League Cup with Leicester City, had a happy return to his old club as the unbeaten Premiership side survived extra time to win 3-2.
It was a happy night for the other Premiership clubs involved as well as Arsenal beat West Brom 2-0, Everton defeated Luton 4-0, and Watford saw off Hull 2-1.
Holders Manchester United begin the defence of their title away to Crewe on Wednesday.
English champions Chelsea are away to Blackburn, Liverpool host Premiership newcomers Reading, Charlton take on Bolton and Newcastle host Portsmouth.
Milton Keynes of League Two, the fourth and lowest tier of the English Football League, host Premiership Tottenham.