The 27-year-old, who had a spell on loan at Deepdale in 2011, equalised for Coventry eight minutes after Graham Cummins had fired Preston ahead in the 30th minute.
A Chris Robertson own-goal after the break then gave Coventry the lead before Nicky Wroe pounced on the hour mark to salvage a point for North End, who have not won at home in the league in 10 matches.
Robins was left bemoaning Coventry's finishing but he is adamant if Clarke, who joined the club permanently this month, performs like he did against Preston he will not be complaining any more.
"Leon is a different type of player from David McGoldrick [who was on loan at the club] but I thought he did really well and deserved his goal," said Robins.
"If he works like that he will get goals - that is what I am looking for. We have to be more clinical, the first goal we scored was a well-worked move and a decent finish.
"We were good value for three points but we didn't get them and if you let players run off you and don't defend properly from a throw in then you get disappointment.
"We did everything else right. We created an unbelievable amount of chances again for an away side and we performed well, performance-wise I am happy.
"The ball gets a headache here at Preston and we coped pretty well with what they had to throw at us.
"They scored from their first meaningful attack and in the second half they have launched the ball and we dropped too deep."