Pardew praised his players for refusing to give up the fight and queried some of referee Robert Madley's decisions - in particular rejecting a Demba Ba penalty claim and then awarding one against keeper Tim Krul.
Pardew said: "I don't like the tag of gallant losers but it was a fantastic effort and the fans would have appreciated the effort we have put in.
"It was a game that had some strange parts to it. We lacked urgency in the first half and I was a little disappointed but after that I couldn't fault my team, I thought we were excellent.
"Some times events just go against you and events certainly did tonight.
"To go 2-0 down was galling as we were bossing the game at that point and we had had a couple of [penalty] shouts. I thought when Demba turned (Chris) Samba it was a penalty, then at the other end Tim plays the ball and is penalised.
"But the players don't know when to give in, we kept going and two great hits got us back into the game, but tiredness cost us at the end.
"If we are going to go out of the cup that's how it should be - giving it everything."