Parkinson's men travel to Aldershot's EBB Stadium on Sunday (kick off 2:00pm) for their first round encounter with the National League side.
This weekend's tie with Aldershot will be the second successive season that City have begun an FA Cup campaign against a side from that division after travelling to near neighbours FC Halifax Town in the first round last year.
Following a challenging first period at The Shay, a second half comeback - aided by the introduction of Billy Clarke and goals from Jon Stead and Filipe Morais - helped City eventually overcome their plucky opponents.
Parkinson reckons the knowledge picked up from that hard-fought encounter, coupled with the memories collected from City's other FA Cup ties during last season's famous run to the quarter-finals, will certainly come in handy as the Bantams aim to avoid a giant-killing at the weekend.
The City chief said: "We obviously had a terrific run in this competition last season and we embark on another challenge down at Aldershot on Sunday, looking to make some more good memories for ourselves and our supporters.
"We have to cast our minds back to the start of this competition last season when we played Halifax away.
"That was a tough game for us - a massive test for us on the day - and I am expecting Sunday's match at Aldershot to be exactly the same in terms of the amount of effort and professionalism we'll have to show to get into the next round.
"We have to accept the expectancy levels that will be on us come Sunday given what we achieved last season.
"Aldershot will have a big home support there I would imagine, their players will be really up for the game, and we will have to be the same.
"We have experience of being the underdog and being the favourite in cup games. We have to use all of the knowledge we have gained over the last three or four years in the case of the guys who were also here for the Capital One Cup run to make sure we are really prepared for this game."
Facing up to Aldershot on Sunday, City may well come up against a familiar face in the home ranks.
Former Bantams defender Luke Oliver may start the tie for Aldershot after coming off the bench to replace injured centre half Jack Saville in the first half of their previous league game.
Oliver was named City's Player of the Year in Parkinson's first season at Valley Parade but his next campaign - the club's history-makers spell - was ended early when he suffered a ruptured achilles tendon at Burton Albion in October of the that year.
A starting berth for Oliver in Aldershot's defensive ranks could mean an interesting match up against Bantams striker James Hanson after the pair spent nearly four years together as team-mates at City.
Parkinson added: "It'll be a good contest.
"Their battles were always honest and competitive in training and it will be a test for both of them.
"Luke was a terrific character when he was here with us.
"He was unfortunate to pick up a serious injury during his time at the club but he is a really good lad and we look forward to meeting up with him again."
After coming off with a slight injury during Tuesday's win over Blackpool, Reece Burke is a doubt for the trip to Aldershot.
Burke, along with fellow loanees Lee Evans, Kyel Reid and Luke James, has been given permission to play in the FA Cup for City. Evans will miss Sunday's tie, however, as he serves out a one-match ban for picking up his fifth booking of the season against Blackpool.
Parkinson says Burke has been making progress this week but Nathan Clarke is expected to be in line to move up into the side should the young West Ham United loanee not be risked.
Parkinson continued: "He's not too bad at the moment. He's progressing well.
"It was more of a precaution really to take him off.
"There was some caution at the time but he's looking a lot better now. We will assess him tomorrow (Saturday) morning and see how he is."