Halifax have now conceded 10 goals in their last two home outings after their 7-1 humiliation against Cheltenham, and Kelly admitted his team were not good enough again.
“You’ve got to give them (Woking) credit,” he said.
“But they played well because we were the ones that allowed them to.
“I thought at times, like last Saturday, we gave players too much time and too much respect on the ball and lost the one against ones you should win, especially at home.
“You’re getting fantastic support, spending their well-earned money to support you up to the hilt and they don’t deserve what they’re getting.
“But I will change it and make sure that, come the end of the season, we’ll not be where we are.”
Woking belied their awful form of four defeats on the bounce with a bright opening 10 minutes, which was capped with Dan Holman tapping-in unmarked at the far post from Kadell Daniel.
A deserved second arrived when John Goddard skilfully curled his free-kick around the wall and out of Glennon’s reach.
There were echoes of Cheltenham two minutes later when Town failed to react to a loose ball 30 yards out, with only Holman alive to it as he curled a sumptuous shot beyond Glennon.
Halifax: Glennon, Bolton, Banton, Brown, K Roberts, Bencherif (Macdonald 87), Sadlier, James, McManus (Hamilton 55), Burrow, Tuton (Hughes 55). Unused substitutes: Porter, Brooks.
Woking: Cole, Caprice, Ricketts (Poku 85), Saah, Arthur, Jones, Murtagh (Keohane 87), Thomas, Goddard, Daniel, Holman (Sole 68). Unused substitutes:Andrade, Hamann.
Referee: Stephen Ross.
Man of the match: Dan Holman
League One rivals Bradford or Barnsley will host fourth-tier York City in the Johnstone’s Paint Trophy quarter-finals.
The original second-round match between the two Yorkshire clubs was postponed due to a waterlogged pitch at Valley Parade and will be played tomorrow night.
Elsewhere in the northern section, Rochdale host Morecambe at Spotland and Sheffield United travel to lowly Fleetwood. Wigan are at home to Blackpool in an all-Lancashire tie.
In the sourthern section, Gillingham have been handed a home draw against Yeovil, while Dagenham host on League Two rivals Oxford at Victoria Road.