The Eagles saw the Blues lift the Premier League trophy aloft after the match but Pardew felt the only goal of the contest came in dubious circumstances.
Hazard stepped up to the spot only to see his attempt saved by Julian Speroni before the ball rebounded nicely for him to head home, leaving Pardew frustrated.
"I do feel a little bit hard done by," Pardew said.
"It was kind of questionable. Then they get another break when he misses it and it goes straight to him."
The defeat leaves Palace sitting 12th on the Premier League table with three fixtures remaining.