The visitors went ahead through a Danny Rose strike after 23 minutes, but Kaid Mohamed's introduction sparked Cheltenham's revival and Paul Benson looped a header over Shots keeper Jamie Young midway through the second half for the equaliser.
Aldershot were then forced to hold on with defender Anthony Tonkin picking up a second yellow card 17 minutes from time.
"It's a tough place to come," said Holdsworth. "Cheltenham are a good team with some good players, so we have to be pleased with a point.
"It showed that we have some character and some resilience in the side. It was a big test and they have put in a massive shift.
"I told the players to make it a big week with a home game against Torquay coming up which will be our next cup final."
Tonkin's dismissal followed two fouls on former Aldershot winger Jermaine McGlashan.
"The thing is I know Jermaine very well and I know what he does," Holdsworth added.
"There was nothing Anthony could do - he just stood there. The problem is that the referee has not played the game. Jermaine wins you a lot of fouls and that's the game. We're grateful that we've not suffered too much."