The visitors remain unbeaten so far this term following back-to-back wins against Coventry and Morecambe, in the Capital One Cup, but Parkin was left disappointed after the Banks’s Stadium game despite a second successive clean sheet.
Parkin said: “We were very disciplined and good tactically, and in the second half I thought we were excellent in restricting Walsall to the one effort at the end when Jordan Pickford made a great save.
“I was a bit disappointed with us going forward, though.
“We didn’t move the ball around as quickly and as well as we did in the Coventry game.
“We got in some good situations in the final third, but there was just something lacking.
“We never quite finished it off.”
Striker James Hanson came closest to a winner for the Bantams when he planted a header inches wide.
However, the visitors were indebted to Sunderland loan goalkeeper Pickford late on when he saved brilliantly from Adam Chambers’s thunderbolt shot.
Mark Yeates and Billy Knott had gone close for the visitors, and Mason Bennett, the loanee from Derby making his Bantams debut, was denied by a smart combined tackle from Liam Kinsella and James Chambers.
Andy Taylor volleyed inches wide for the Saddlers after chesting down from Rory McArdle’s fluffed clearance.
Walsall: O’Donnell, Downing, Chambers J (Holden 70), Kinsella, Taylor, Sawyers, Grimes, Benning (Forde 75), Chambers A, Clifford, Bradshaw. Unused substitutes: Baxendale, MacGillivray, Flanagan, Morris, Bakayoko.
Bradford City: Pickford, McArdle, Meredith, Darby, Davies, Yeates (Shariff 76), Liddle, Knott (Dolan 66), Kennedy, Bennett (McLean 64), Hanson. Unused substitutes: Williams, Routis, McBurnie, Morais.
Referee: D Whitestone (Northants).
Man of the match: Mark Yeates.