The Cards boss was angry with referee Simon Beck's decision to send off central defender Tom Hutchinson for a professional foul - a moment which cost Woking a vital player and a goal as Ben Strevens stepped up to give the visitors a 10th minute lead from the penalty spot.
Cockerill's men battled back to draw level through Craig McAllister after missing a penalty themselves, but Crawley defender Dave Woozley's second-half winner helped maintain the Sussex outfit's 100 per cent record this season.
Crawley started well and Strevens cracked an effort narrowly wide in the opening minute before the dramatic moment in the 10th minute which had a huge bearing on the contest.
Former Telford and Exeter striker Jake Edward burst clear into the box and as he went to go round Woking keeper Shwan Jalal, Hutchinson was adjudged to have brought him down.
Referee Beck had no hesitation in pointing to the spot while he showed the Cards defender the red card.
Strevens took great delight in stroking the penalty beyond Jalal's left hand to put the visitors ahead.
The Cards were forced to reshuffle and skipper Neil Smith was sacrificed as Karim El-Salahi was brought into the fray to partner Gary MacDonald in the centre of defence.
With Tony Scully, Strevens and Edwards a threat going forward, Crawley looked dangerous in attack while Woking tried hard to get striker McAllister into the game with long balls forward in the hope that Liam Cockerill and Steve Ferguson would feed off the knock-downs.
The hosts felt they had a penalty themselves when McAllister went down under a challenge from Ben Judge, but Beck was unimpressed sparking angry scenes on the Woking bench, Cockerill senior hardly managing to contain his feelings.
Just before the break Woking had their chance to level it up. A wonderful pass from Shola Oyedele split the Crawley defence and found Simon Jackson on the right byline. His cross saw Crawley's Lee Blackburn shove McAllister in the back, but the striker hit the resultant penalty against the inside of the post.
McAllister got his goal though, right on the stroke of half-time. Another superb pass from Oyedele picked out Cockerill on the right. The manager's son floated over an inviting left-footed cross and McAllister rose majestically to power a downward header past keeper Ben Hamer.
It was no more than the hosts deserved and they would have been relieved to go in at the break on level terms.
With the extra man Crawley started the second half much the stronger, despite losing Edwards at half-time with a neck strain. Gary Mills had a shot charged down by MacDonald and a minute later, 15 minutes in, Crawley defender Woozley thumped his side back in front from a Blackburn corner.
It might have been 3-1 moments after that, Strevens collecting a pass from Scully before hitting a fierce low drive that had Jalal stretching to divert left-handed around the post.
Woking's influential midfield man Karl Murray made a unexpected appearance as a 72nd minute substitute, having recovered from a knee injury, but Crawley's policy of keeping the ball was right from their point of view, with Woking tiring in their vain efforts to get back into the game.