Ward admitted his side never got going during a low-key affair against lower-league opposition and is hoping for better in tomorrow night's replay.
"We played too many long balls, which played right into Biddulph's hands," he said.
"All credit to them, though. This is their cup final and they did well to keep our forwards quiet.
"We played really well in the week to win at Glapwell, so I was disappointed we couldn't keep that run of form going.
"But that said, we're still in the competition and we know if we play to our potential we'll get through."
The result was even more remarkable since Midland Alliance outfit Biddulph were without regular keeper Gary Goodwin.
His replacement was former Leek Town forward Steve Brannan, and he looked like being tested inside a minute until Dave Walker scuffed his shot wide.
Biddulph settled down after that to play some excellent one-touch football against their Evo-Stik League rivals and they were almost rewarded on 13 minutes, but James Marrow headed a Chris Leigh cross wide of the Kidsgrove goal.
Chris Coleman also went close for Vics soon after when his looping curled effort from the right-hand edge of the Grove box flew narrowly wide.
Kidsgrove had a penalty appeal turned down on 20 minutes when Liam Shotton tangled with Leigh in the box.
Shotton then produced a weak half-volley from the edge of the Biddulph penalty area that didn't test Brannan.
Vics were indebted to defender Kieron Ellis 11 minutes before the break when he was on hand to clear Shotton's goal-bound effort off the line.
Vics could have snatched the lead themselves before half-time when Paul Bowyer powered a header towards goal from a Tristan Hamilton corner, but Danny Smith was on hand to clear off the line.
Nick Ward thought he had opened the scoring for Grove on 63 minutes, but his header from a Tim Sanders corner was ruled out for a push.
Shotton missed another guilt-edged chance for Grove soon after when he could only direct Ricky Bridge's cross from the left over the Biddulph bar from six yards out.
Vics were still in the game and were inches from going ahead when Leigh's long throw from the right was headed just wide by Marrow.
But Ellis was again the Biddulph hero as full-time approached, clearing Walker's effort off the line after he had rounded Brannan.
Shotton could have won it for Grove in stoppage time when he was played in by Geoff McGaw's ball over the top, but he found only side-netting.
Biddulph chairman Terry Greer praised the commitment of his side and has called for more of the same in the replay.
"It was a terrific result for us," he said. "The lads were disciplined and organised and we were never under any sustained pressure until the last 10 minutes.
"We knew we had to stick to our game plan because they're a good side, but we also created some good chances."
Kidsgrove Athletic: Intahar, Smith, Dove, Ward (Harper, 75), Schwarz, Beasley, Urwin (Matranga, 67), Sanders, Walker, Shotton, Bridge (McGaw, 80). Not used: Pointon, Hall.
Biddulph Vics: Brannan, Leigh, Clarkson, Coleman, Ellis, Bowyer, Mould (Skellern, 79), Quinn, Marrow (Pearson, 79), Baker, Hamilton (Daniel Smith, 78). Not used: Barlow.
Attendance: 183.