Parkinson had told his men to prepare for a full-blooded battle against a Vale side who he realised would be desperate to bounce back from a defeat at Colchester seven days earlier.
But Bradford were second best in the first-half and failed to turn the game on its head despite a much improved second-half display and a grandstand finale in front of 1,150 travelling fans.
Parkinson said: “I warned my players exactly what sort of game it would be because I knew Micky Adams would have his players right at it. It was always going to be full-on and competitive.
“We didn’t handle that too well in the first-half when Vale were better than us in certain areas. We didn’t stop the crosses coming into our box well enough and were put under pressure.
“I was pleased by the reaction in the second-half.”
Bradford had looked full of confidence in the early stages at Vale Park as Nathan Doyle’s ferocious volley was deflected wide, but Vale soon responded in a wide open and physical contest. Bradford goalkeeper Jon McLaughlin made smart saves from Lee Hughes and Kaid Mohamed before Vale’s pressure told.
James Meredith rolled an intended back-pass straight into the path of Hughes and the 37-year-old made no mistake as he rounded McLaughlin and slid the ball into an unguarded net.
Bradford equalised in the 59th minute after a brilliant piece of skill by Nahki Wells. His initial effort was blocked after he had left two defenders trailing, but Wells prodded in the loose ball following a follow-up shot from Garry Thompson.
But Vale’s winner arrived seven minutes later when Doug Loft struck a 20-yard shot from Hughes’ lay-off and the ball took a deflection to beat McLaughlin.
Port Vale: Neal, Yates, Robertson, Dickinson, Jones; Myrie-Williams (Griffith 90), Loft, Lines, Mohamed; Hughes (Dodds 90), Pope. Unused substitutes: Tomlin, Shuker, Williamson, Duffy, Birchall.
Bradford City: McLaughlin, Darby (Connell 88), McCardle, Davies, Meredith; Thompson (De Vita 71), Doyle, Jones, Yeates (Reid 71); Wells, Hanson. Unused substitutes: Ripley, Taylor, McHugh, Ravenhill.
Bradford man of the match: G Thompson.
Referee: C Boyeson (East Yorkshire).