Goals from Lewis Gibbens, Steven McDonnell and Aaron Sennett-Neilson ensured passage into the next round where they will travel to Bromsgrove Sporting on Saturday 18 September.
And Parry believes they bounced back well from Monday’s 2-1 defeat against Frickley Athletic.
“I thought we played extremely well today,” said Parry.
“We’ve had a tough week; there were some harsh words said at training Thursday. Some clips were shown to the team, and they’ve come in and dusted themselves down and played as a team.
“We created an unbelievable number of chances; the chances we’ve created today are probably the most we’ve ever created in a game.
“If I’m saying a negative, it’s that we’ve got to be a little bit more ruthless. We could’ve been a little bit cutthroat in the early stages.
“It’s also about doing the ugly side and putting it in behind them and asking questions about them, which I felt was a perfect mixture for us today.
“We knew these guys [Newport Pagnell Town] are a good team. We looked at their results and the goals they scored, and we knew they wanted to play out from the back, so we made changes to put another extra body up the pitch.
“I tried to be a little bit more aggressive on the front foot, and I thought our two ‘number tens’ today Bax [James Baxendale] and Aleks [Aleksandrs Starcenko] were unplayable.
“I was pleased with how they played; I was also pleased with how the team moved the ball.
“The third goal was a great ball in from Macca [Steven McDonnell] for him to spot Aaron [Sennett-Neilson] and Aaron is on fire at the minute; he whistled on into the top corner and it’s a good goal for the fans to see.”
McDonnell has now scored five goals in his last five games.
The forward believes Worksop made many opportunities and that the goals will come.
“I thought we played well,” he said. “I didn’t think we played that bad on Monday to be fair.
“We continued to pass the ball around very well.
“We created a lot of chances again today, so hopefully, sooner rather than later, those chances will be converted more, and we can beat someone six or seven-nil.”