With new loan signing Mason Bennett making his debut from the start, the Bantams held off everything their hosts could throw at them to secure a goalless draw at the Banks's Stadium.
The Saddlers enjoyed more possession of the ball throughout the contest but they struggled to breakdown a resolute City set-up, with the Bantams themselves probably creating as many clear-cut scoring chances as Walsall.
The point and battling performance comes after an eventful week for a number of City's players, including Gary Liddle, who became a father for the first time, and Bennett, who was involved in a motorway accident this Thursday.
The Bantams themselves were affected as a group in the build up to the Walsall game after being caught up in traffic on the M6 while heading towards their pre-match meal at a Staffordshire hotel.
Parkin said: "This is a very good point for us.
"We've had a bit of a stop-start week leading up to today (Saturday). Obviously the sad news for Alan (Sheehan) about losing a family member, Gary Liddle being caught up in all the emotions of becoming a dad, losing Billy Clarke to injury yesterday (Friday), and Mason Bennett having a bit of a nasty accident in his car Thursday night.
"It has been a really testing week for the lads, coupled with the fact that we've had three games in that week - two of which have been away from home.
"I felt we looked a bit off the pace at times in the first half but we dug in and showed our resolve in the second period.
"You have to be patient as a defence when you come here, and I felt there was some outstanding defensive displays again from us.
"When you have tough games like this after a challenging week like we've had, you have to take positives away with you, and the positive we have from today is the clean-sheet and the commitment from the players.
"This point helps us to keep up our decent start to the season.
"We now have to make sure we prepare the players right mentally and physically for the long journey down to Crawley Monday for the game on the Tuesday.
"Thoughts will now quickly turn to Crawley and that game. We have to make sure the players are fully recovered after today and ready to go for what will be another challenging away fixture."