The Reds were beaten 2-1 at Maidstone United on Saturday and finished the game with nine men - watch match highlights here.
Alex Reid netted Wrexham's opener, his second goal in as many games since signing for the club, but Alex Wynter and Jack Richards soon turned things around for the Stones.
Keates' away day woe was compounded as Manny Smith and Mark Carrington were sent off within three minutes of each other.
That result leaves Wrexham on six points ahead of Saturday's home game.
"We need a reaction. We have had it in the past at Gateshead and Maidenhead, we need it at home now against Woking," said Keates.
"We’ve already won one at home and we want to make it a fortress. We are still finding our feet, I would have loved it to fall into place from day one, I didn’t envisage it being like this, but we will keep working hard and all being well we can put a run together starting at the weekend.
"It is a new team - we have gone on record saying they know each other, one or two have crossed paths at different clubs, but this is an entirely new environment coming to a new club, a new set up.
"But they know what we want and how we want to play, with the ball and without the ball, and it is a case of keep sticking to our philosophy and all being well it falls into place.
"It has been frustrating, but the lads will keep going and we will keep pushing them."