Nathan Dyer gave the hosts a 1-0 lead in first-half stoppage time before Mathieu Debuchy's own-goal doubled virtually ended the game as a contest 67 minutes in.
Jonjo Shelvey completed the scoring eight minutes from the end, despite Pardew feeling the former Liverpool man was lucky to still be on the pitch after an altercation with Debuchy.
Pardew believes his side were unlucky to lose by such a margin and that Webb's display proved decisive in seeing Newcastle's run of four consecutive wins come to an abrupt end.
He said: "I didn't think we deserved that. I was a bit disappointed we didn't keep a clean sheet until half-time, although we didn't retain the ball very well. In the second half we pushed on and we created chances.
"Two big decisions have gone against us – (our) first penalty claim was a penalty, I've no doubt about that. I felt it at the time and my players' reactions told me all I needed to know.
"It hit his (Ben Davies') arm when it was going into the net. That's a penalty, isn't it? He (Webb) said the ball hit him on the arm, but he didn't move his arm towards the ball."
The 52-year-old also questioned the decision not to award a free-kick for a foul on Yoan Gouffran in the build-up to Swansea's second goal.
"That was from a foul on Gouffran," he added. "I thought (Ashley) Williams had no chance of winning that header. He went into the back of Gouff and he (the ref) has played on.
"I accept Webb's explanation but don't agree with it. Then there was an incident with Jonjo (Shelvey), which after looking at the highlights was a bit disappointing for him. You could argue he shouldn't have been on the pitch.
"We had one of those nights where all those things went against us and that impacted on the score."
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