They was just a minute remaining of the eight signalled for stoppage time when Bradford were awarded a penalty after Terrell Forbes tripped winger Zavon Hines.
Substitute Alan Connell duly equalised from the spot, cancelling out Kieron Cadogan's first-half opener, to secure a last-gasp draw.
Play-off hopefuls Bradford have taken only two points from their last five home matches and are now nine points off the top seven but Parkinson remains upbeat.
"We couldn't have done more than we did," he said. "In the first half we played really well and had chances but Jamie Young produced two really good saves.
"I thought their goal from a free-kick was a soft goal. It was their first real attack, they took a free-kick and it has ended up in the back of our net.
"A goal just before half-time gives the other team a lift, but at half-time we didn't feel disappointed for ourselves. We came out and did everything we could. We kept driving forward, we played our attacking subs and the goal finally came in the 97th minute.
"I thought the lads were fantastic and to have got beaten would have been a travesty. I thought Alan Connell was outstanding when he came on and I was pleased when he got hold of the ball and took the penalty.
"That was a tough game. Aldershot put themselves on the line, they are fighting for their lives.
"This season is very much alive for us and we will make sure it stays there."
- Sports & Recreation
- Alan Connell
- Zavon Hines