Grayson is still searching for his first win at the helm after succeeding Stuart McCall.
Eight games without a win has left the Bantams outside the play-offs.
Antoni Sarcevic scored the only goal of the game before Charlie Wyke was sent off at the end to leave the Bantams without a win since New Year’s Day.
Grayson said: “Neither goalkeeper had a lot of saves to make. That was the story of the game.
“The goal was a deflection and that knocked the stuffing out of us. It was disappointing that when we had the ball we gave it back cheaply.
“I’m disappointed we didn’t get something out of the game.”
Colin Doyle had to be alert early on to deny Plymouth’s Ruben Lameiras.
Paul Taylor came closest for the visitors, forcing a couple of saves from Remi Matthews.
The goal came after 34 minutes as Sarcevic’s deflected effort evaded Doyle.
It was almost two later in the half when Lameimas blasted an effort just wide.
After the break, Graham Carey beat three Bantams defenders before missing the target and City captain Romain Vincelot kept the deficit to just one with a sprawling block on the line to keep out Sarcevic before Tyrell Robinson missed a glorious chance to equalise when he failed to divert Alex Gilliead’s cross on target.
Late on, Wyke was shown a straight red for an elbow on Sonny Bradley.
Plymouth Argyle: Matthews, Threlkeld, Vyner, Bradley, Sawyer, Sarcevic (Songo’o 86), Fox, Ness, Carey, Taylor, Lameiras (Taylor-Sinclair 85). Unused substitutes: Makasi, Letheren, Grant, Ainsworth, Church.
Bradford City: Doyle, McMahon, Knight-Percival, Kilgallon, Warnock, Gilliead, Vincelot (Lund 69), Guy, Chicksen (Robinson 59), Taylor (Poleon 59), Wyke. Unused substitutes: Raeder, McCarten, Dieng, Law.
Referee: G Salisbury (Preston).