Alex Neil wants more from Preston despite seeing his side move into third place in the Championship with a 2-1 victory over Luton.
But the hosts were made to work for the points, with James Collins equalising from the penalty spot before former Luton loanee Stockley struck late on.
"Luton are fighting and scrapping for points all the time," said Neil. "I've watched some of their games and there's not been a lot in them.
"Our biggest error was letting them back into the game. When we got the first goal, I thought that's the breakthrough you need against the likes of Luton.
"Make them have to come out and try and get the goal to equalise and then you can hurt them. It didn't transpire that way.
"I thought we were a bit slow in our build-up, I thought we were a bit sloppy, and I thought our two wide players rolled down the pitch too much, because then my full-backs had to go really high to offer us width and that left spaces down the sides for them to counter.
"I thought Luton's penalty was really soft. I've seen it back and I thought it was a poor decision, but we allowed him to make a decision by being sloppy further up the pitch.
"The most important thing is we won't be talking about this game in a week's time – we'll be talking about going to third, so that's the most important thing."
Preston were ahead inside five minutes, Matty Pearson pulling Patrick Bauer's shirt at a corner though Gallagher had to convert the rebound after James Shea's initial penalty save.
They rued the missed opportunity when Stockley fired home from close range in the 84th minute.
"On 80 minutes Cornick runs through to make it 2-1 and I think Pelly (Ruddock) had a good chance as it comes back to him, then it's a very different game," said Luton manager Graeme Jones on the match's key moment.
"I think where we are at the minute, that's probably how it goes.
"We've got to fight and earn the right to be in a stronger position next season. I know where we are and I don't want to lose football matches because a draw was a fair result.
"There was nothing in the game and remember, Preston have gone third. This is some away ground to come to and we had a right go, we competed.
"I let them know that's what I wanted more than anything, because the midweek defeat to Stoke was very, very disappointing.
"I changed the shape, got a massive reaction from the group, so that aspect is satisfying because if we continue with that, I will never let it drop.
"I've told the players 'you need to police it'. Don't ever let it drop again, that's minimum requirement, then I know it's a step forward and I know we'll get results away from home."