Yoan Gouffran gave Newcastle a deserved half-time lead, but Southampton improved after the break and earned a point thanks to Jay Rodriguez's superb goal.
In an open contest, Remy wasted Newcastle's best two openings when he saw his first-half effort kicked off the line by Calum Chambers before he missed a gilt-edged chance in the second after being gifted the opportunity by Southampton goalkeeper Paulo Gazzaniga.
Pardew admitted the misses proved to be the difference in the game as Newcastle had to settle for a share of the spoils.
"It was a real Premier League game, good teams at it, but Southampton have got a great defensive record and we had two massive opportunities with Loic," Pardew told Sky Sports.
"I thought he [Remy] played well today, but those two you would expect him to score and at this level it would have made the difference.
"The rest of the game was very, very tight - they had periods, we had periods - two good teams."
Pardew admitted the introduction of Adam Lallana at half-time helped turn the game in Southampton's favour, but felt his own substitute Hatem Ben Arfa could have won it for Newcastle.
"I thought Adam Lallana had an impact on the game, for sure, but having said that so did Hatem [Ben Arfa], he could have won it for us at the end. He made a few nice moments for us.
"That's what these players are paid to do if they are not in the team - come off the bench and make an impact."
Pardew felt his side missed the presence of the suspended Yohan Cabaye, even though his replacement in midfield Vurnon Anita produced a decent performance.
"I thought he [Anita] played well, we certainly miss Cabaye's quality and that pass to unlock the door and that composure. In a game like that those players are gold dust and fortunately for us he is back next week."
Referee Mike Jones suffered a bloody nose late on in the game after Moussa Sissoko accidentally slapped him in the face and Pardew felt the incident did not need to be taken seriously.
"It was a bit panto season towards the end," continued Pardew. "It was amusing and the ref has taken it in good heart.
"It was an accident. He got a bloody nose and he will have to tidy himself up for his Christmas party."