Preston caretaker boss John Dreyer will not push for the job on a permanent basis despite his side's 2-0 defeat of Bournemouth.
Westley was sacked as manager after 13 months in charge at Deepdale on Wednesday with the side having won just once in League One since November.
But Stuart Beavon lifted the gloom with a fine strike after 19 minutes and Bailey Wright doubled the lead before the break to end leaders Bournemouth's run of five successive wins.
Dreyer, installed as caretaker boss on Thursday, said: "I really enjoyed it, from Thursday onwards we've had a strange week, but it was a top performance.
"I wanted them to play football, the surface was tricky, but I didn't want that to worry them and they played good football and were disciplined.
"My remit on Thursday was to take charge of Saturday's game and I was so focussed on the game I've not thought of anything else.
"My time here could be over, but I wasn't looking beyond the game.
"I certainly have aspirations of being a manager, talking with players and being around them isn't an issue. I won't be badgering the chairman for an answer, I'll be speaking to him for sure, but for all I know there could be a new man coming in."