Pardew hard done by after Saints defeat
Southampton secured maximum points when Sadio Mane took advantage of a Julian Speroni error seven minutes from time, after Palace had earlier hit the post through Wilfried Zaha.
Defeat ended a run of five consecutive away wins for Palace in all competitions since Pardew took over, but the former Southampton boss felt his team should have had a penalty for Jose Fonte's challenge on Yannick Bolasie.
"In the first half Southampton were by far the better side in a game they had to win," he told BBC Sport.
"Second half we were the better team and had two great chances. We also should have had a penalty and it is so disappointing we have let in a soft goal.
"Our keeper Julian Speroni is big enough to hold up his hand but we should have stopped it before it got anywhere near there [James Ward-Prowse firing in a shot that the goalkeeper spilled].
"Jose Fonte is over-aggressive on Yannick Bolasie and I think we should be given that.
"The performance level was high. We are disappointed we haven't come away with a point, because we think we deserved it.
"We had little protection from the referee because the centre-halves were coming through our strikers, which they do here."