Cavaleiro had slipped and shanked a spot-kick over the bar in embarrassing fashion against Everton last month, but he stepped up again to score what turned out to the winning goal from 12 yards as Fulham stunned Leicester to move out of the relegation zone last night.
Fulham had missed their previous three penalties and Parker praised Cavaleiro after he ended that hoodoo.
Parker said: "Last week, he slipped taking the penalty. I am not on Instagram or Twitter but I can only imagine what was being said, the jokes and the laughter at one's expense.
"We practised penalties all week and I asked him if he was ready to take this penalty if we get one. He looked me dead in the eye and said, 'Yeah, I am ready'.
"The courage, the bravery after a slip and some of the things he has probably seen that have been said about him, to step up… they are the things that we need. They are the things that will determine what we become."
Ademola Lookman also scored against Leicester, three weeks after he was widely criticised for a failed attempt at a Panenka-style penalty at West Ham.
"There is no denying there's relief," said Parker.