Cudworth was making his debut at the Weaver Stadium just hours after signing for the Dabbers.
But calamity struck in the 11th minute when he was judged to have felled Josh Hine, who stroked home the spot-kick.
Cudworth told StaffsLive later: “It wasn’t a penalty.
“I mean the linesman’s even said to me that he’d seen me get a hand on the ball.
“The referee’s not in the best position to give it. He seemed to want to get involved quite a bit, but you’ve just got to get on with it.”
Cudworth was signed by Nantwich boss Danny Johnson at 7pm on Monday (October 14) to replaced injured first choice keeper Terry Smith.
Johnson said: “I don’t think he has had much to do apart from pick the ball out of the net after he conceded the penalty, which we don’t think was a penalty.
“I can’t think of a shot that he has had to save.”
The 21-year-old started his career at Preston North End, working his way through youth system at Deepdale to the reserve side.
He added: “It was a bit strange playing Chorley because I know them all so well, but I play for Nantwich now so I was trying 100% to get a win.
“At the end of the day we’ve banged on the door and not scored, so that’s football. You get bad decisions from time to time, it’s just how you react to them.
“All the lads and staff seem really friendly so I’m looking forward to playing, getting a few games under my belt and hopefully we can go on and get some wins.”
Boss Johnson, added: “Terry Smith could be out for the season we think. He has ruptured his knee through the thigh, which is a grade three, so hopefully Jack will come in and do as well as Terry has done.”
Chorley’s Dale Whitham was shown a red card for a dangerous challenge on Oliver Devenny after 26 minutes.
But a well-organised, ten-man Chorley hung on for a 1-0 victory as the Dabbers went on the offensive.
Cudworth, had little else to contend with as Aaron Burns’ free kick was poked over the crossbar, then Russell Courtney headed wide from a corner.