Clarke missed a string of chances as Wednesday at Selhurst Park, while Neil Warnock's Eagles attack could at least share the blame with Alan Lee, Victor Moses, Paddy McCarthy and Darren Ambrose fluffing their lines in front of goal.
But every Owls opportunity seemed to fall to Clarke, and Laws moaned: "We had more of the chances and they weren't half-chances, they were good ones and Leon had most of them.
"I've said to him, 'You could have played all night and not hit a barn door'.
"I think Neil will be disappointed with his team's finishing, and I'm definitely disappointed with ours because we've scored some good goals of late.
"But our finishing boots were definitely left in the dressing room tonight."
Unfortunately a game which promised much, with Palace having beaten leaders West Brom on Saturday while Wednesday were seeing off Cardiff, delivered precious little.
Palace passed up four chances in the opening 20 minutes with McCarthy firing over, Ambrose missing his kick, Moses driving wide and Lee somehow sidefooting the wrong side of the post from in front of goal.
Clarke hit the side-netting and fired over before the break, and was denied by Julian Speroni as he broke clear shortly after the interval.
The big striker was gifted another chance by Speroni, who spilled a cross at his feet, but he skied his effort.
"Sometimes you are not going to get a free-flowing game and you have to grind out a result, and we ground out a result today," added Laws.
"I don't think Neil will take it the wrong way but it reminded me of playing Sheffield United. They get the ball forward quickly and make things happen, and we have shown that we can deal with that."
Palace have registered just two goals in five league matches this season, and have not hit the net in the first half in their last 19 games.
"We had some good chances but we snatched at everything, we just don't like scoring in the first half," said Neil Warnock.
"We are lacking in quality but I don't think they were any better. I can't fault the lads, they are giving me everything.
"We could not put our chances away, it's as simple as that. But we've got seven points from three games and all credit to the lads for that."