The Lilywhites saw the appeal rejected in terms of the sending-off but the winger’s suspension was cut from three matches to one.
Neil addressed the subject at his pre-match press conference to look ahead to Sunday’s visit to Brentford, a game which Barkhuizen has to sit out.
“I think it’s still disappointing,” said Neil.
“Looking back at the challenge there is no intent, Tom didn’t even intend to go in for the challenge, never mind hurt the lad.
“It is one of those ones where they obviously didn’t think it was meant but instead of going the whole hog and rescinding it, what they have done is reduced the ban.
“They probably think it is a halfway house but for us it doesn’t really help for the next game.
“So there is still some frustration from our point of view.
“One game is better than three but there was no intent from Tom whatsoever.”
Presumably, the challenge will go down on the FA’s file as having been reckless as the red card was left in place.
The one-match ban, though, in normal circumstances is given for a sending-off for two yellow cards rather than a straight red.
Said Neil: “If Tom goes in for the challenge and they deem it to be reckless, then by all means he is rightly sent off.
“But I don’t think Tom means to go in for the challenge, he slips and falls into the tackle.
“That is where my frustration comes in.
“There was no intent, hence they have reduced the ban.
“What they are trying to do is back the ref up with his decision but equally understand it has probably been harsh on us.”
This was completely out of character for Barkhuizen, with it being the first red card of his professional career.
In his 153 appearances for North End, the 27-year-old has only been booked five times.
So for anyone to have viewed his tackle as being deliberate in any way, was the wrong approach.
Barkhuizen’s absence will mean a rejig of the frontline for Neil at Brentford.
He played as a wing-back against Stoke in a 3-4-1-2, so a switch to 4-2-3-1 would see Joe Rafferty play at right-back and give Neil options to change higher up the pitch.