The Tigers came from behind to advance to the first round proper of the competition, with a Liam Hughes double - the second from the penalty spot in the sixth minute of second half stoppage time - helping them to victory.
Saturday's brace saw Hughes take his tally to a remarkable 56 goals in 56 appearances for Worksop.
Twelve of those goals have come in the 31-year-old's last seven matches in all competitions.
The Tigers will host Mickleover in the next round later this month, but boss Parry insists his squad must learn to respond better when faced with difficult scenarios on the pitch, having left it late to overcome a Steels side struggling for league form in the Pitching In NPL East Division.
“I thought we were poor today. I told them at half-time in no uncertain terms and I told them at full-time," he said after the match.
“The lads get a lot of praise from me when they do well, but today just wasn’t our day in the way we wanted to play.
"They made it extremely difficult for us, but we moved the ball too slow, we got frustrated and lost a lot of battles in there. The win is great, we’re through to the next round but we need to be better than that.
“Coops [Paul Cooper] made some fantastic saves in the game, especially when we went 1-0 down because if we went 2-0 down, I believe it would have been game over and we wouldn’t have got back into it.
“We needed something to spark us, and it actually helped us to concede. If that didn’t happen, I feel like we would’ve still gone through the motions and kept it at a slow process.
“It’s a massive positive that we’ve shown our character and won the game. We know this team has done it time and time again, but when our chips are down and things are not going our way, we find a way to win.”
Alongside Worksop in the FA Trophy first round are 17 more Northern Premier League sides from Step 3/4 level.
There will be five all-NPL ties, with the winners being joined at the second round stage of the competition by teams in the National League North and South.
Photo credit: Darren Murphy