Matt Richards converted a late penalty after Marvin Morgan was brought down in the area by Ben Davies to leave Preston without a home win in the league since September.
The Lilywhites looked like they were going to end that run when Stuart Beavon scored his ninth of the season after 43 minutes but Jon Taylor equalised and Richards wrapped it up.
"There were some strong passages of play and on a different day it could have been a very different result," said Westley.
"I don't think you can expect to be the manager of a club in this league and not win games and have people happy. It's realistic to expect people to want your blood when things aren't as everyone would want them to be.
"When it doesn't go right you have to be strong and you have to focus on the job you need to do. Nobody wants to walk away from a football ground with yet another defeat.
"I think it's difficult for any player to go on a field of play when there's a sense of disappointment around, but when you come to a club like Preston North End it's all part of the process.
"I think that as we go forward that group of players will not put in performances like that and go away with nothing on a regular basis. There's a lot to be encouraged about."
- Sports & Recreation
- Matt Richards
- Marvin Morgan