North End dominated the first period in particular but went in behind to Will Vaulks’ well-struck free-kick from distance on the stroke of half-time.
It was 2-0 when Michael Smith headed home 15 minutes from time, Lukas Nmecha reducing the arrears shortly after.
PNE pushed for a leveller but couldn’t find a way through as Neil’s injury-hit side slipped to a third defeat in four games.
“People will look at that result probably think we didn’t perform,” said the North End manager, who felt Matt Palmer should have seen red for felling Tom Barkhuizen when through on goal early on.
“I thought that was far from the case.
“In the first half if they were 4-0 down and down to 10 men, I don’t think anyone would have batted an eyelid.
“But the simple fact is we didn’t take the opportunities that were created and as so often happens in football we paid the price for that.
“I think their first shot at goal is the free-kick that ends up in the back of our net.
“It’s always difficult after that because Rotherham will have gone in knowing they haven’t performed well, knowing they’ve been dominated and knowing they should be losing the game.
“But as a footballer, when you go in when you haven’t played well and you’re winning there’s no better feeling because you know you’re going to improve in the second half and you’ve got something to hang onto.
"That was our frustration."