But Wednesday still had the better of a low-key game and would have won but for the agility of City goalkeeper Dean Gerken.
Laws said: "We had five out with the virus, two just recovered and two more carrying it.
"Tommy Miller had to come off because he was feeling ill and I had already gone from plan A to plan F in considering my team.
"For all that, the lads out there gave everything and we had the best chances. It was a great point for us in the circumstances, but we definitely deserved to win.
"We were denied the most blatant penalty you could ever see and things didn't quite go for us on the day. I feel a performance like that is one we could build on and it could signal a turning point for us."
Two Crewe old boys, Nicky Maynard and Luke Varney, shared the goal honours in the second half, both producing confident finishes.
Maynard fired City ahead from close range on 59 minutes after wriggling free in a crowded box to clip the ball past Lee Grant.
Varney had missed the best first-half opportunity, shooting tamely at Gerken. But there was no mistake on 75 minutes when he lashed a right-footed shot past City's keeper from 18 yards after being put through by Marcus Tudgay's pass.
Wednesday were convinced they should have had a spot-kick when City centre-back Jamie McCombe was guilty of a clumsy challenge inside the box 20 minutes from time.
It would have been no more than the visitors deserved as Gerken made a good early save from Miller and better stops in the second half to deny substitute Leon Clarke on two occasions and Varney once.
City boss Gary Johnson admitted his team were unrecognisable from the one who clinched victory at Barnsley seven days earlier.
"We nicked a point today because we were all at sea for most of the game," he said.
"It's not often we play like that and we have a tough week of training ahead before our next game with Nottingham Forest.
"For some reason we looked disorganised and lacked the sharpness of thought you need at this level.
"I made a couple of changes at half-time because I couldn't delay them any longer. But we were never at the races and in the end it's a good result for us on a bad day."