Leon Clarke 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.
"We got beaten by a bunch of kids against Walsall so it was a good opportunity to see what ours could do," said Westley.
"Any winning team is about ingredients, things haven't quite been going our way and they need time to revitalise.
"I tried to inject a little bit more of what we needed with [Paul] Connolly's composure and I think we performed credibly.
"It is tough when there is a negative feel but it was a good answer from the lads, they need to show the club they are good enough to help it towards their ambition.
"We don't want to be enjoying a draw with Coventry but we are in a building process and we are pleased to be nicking a point against a big club in form."