The Lilywhites trailed at half-time after Sky Blues midfielder James Bailey had swept home Gary McSheffrey's cut back in the 21st minute. But they had the better of a competitive second half and equalised with 13 minutes to play when Lee Holmes raced through on goal and confidently fired into the bottom corner.
Coventry substitute Stephen Elliott had a great chance to win the game late on when Preston goalkeeper Thorsten Stuckmann flapped at a cross, but the Irishman headed wide.
Westley said: "We battered them, let's be honest about it. I think there was one team out there playing to win and 54% possession in our favour and 12 attempts to six in our favour tells you that. We did a lot to try and win the football match and didn't quite get what we deserved.
"The team made the decision that in the second half they were going to do that little bit extra that it takes to win and we played on the front foot with intensity in our attacking and intensity in our defending.
"What was important was the players' attitude to the game. Whatever you do tactically, it is the way the players go about implementing the gameplan that makes the difference and they absolutely made their mind up at half-time that they were going to win that second half. I just wish they had won it by two, not one."
Sky Blues manager Mark Robins was the happier of the two managers at the final whistle as, despite not performing to their best, his side maintained an unbeaten run that now stretches to eight games.
"In the first half we did well and we thought we were the best team and in the second half we weren't, so we have got to be happy with a point," said Robins. "The first half was a lot better because we tried to pass the ball and in the second half we allowed them to dictate.
"When you allow them to dictate, they're not bad at what they do. They try to grind you down, the ball is in the air forever, they play on second balls, they have been physical and they are different from what our players are used to playing against - but hopefully they have learned."