The focus of Neil's frustration was an early penalty given away which Lewis Grabban scored to give Forest the lead.
They had been caught on the counter attack after giving the ball away near the Forest box, with Ben Pearson then bumping into Nuno Da Costa to concede the spot kick.
North End got back on level terms through Jayden Stockley's close range finish in the 15th minute.
The best fans photos from Preston North End's 4-1 win over Huddersfield Town in the Carabao Cup.
Manchester United youngster being tested by Preston North End on a 'daily basis' after sparkling debut
Preston North End boss provides injury update on Manchester United loanee and addresses specualtion linking them to another Red Devils youngster
Player Ratings: Huddersfield Town 1-4 Preston North End - Carabao Cup win on the road
Wigan remain Championship relegation candidates but bookies' odds drift for Preston North End and Blackpool
After that, the home side had the game's better chances but couldn't find a winner.
Neil said: "We wanted to try and win the game but we made it really difficult for ourselves by giving a cheap penalty away.
"We set up 4-4-2 because we wanted to get the ball up quicker to Jayden but for whatever reason in the first couple of minutes we got roped into playing it short and sideways across the pitch.
"They nicked the ball and we were too open down the left hand side, it was a poor one to give away.
"You know Forest aren't going to give much away so the first goal against them is always important.
"Defensively they put a lot of players behind the ball and make it really difficult to break them down and it has been the same all season for them, so we knew the first goal was crucial.
"By conceding first we made it difficult for ourselves.
"We got the goal back which was a well-worked goal and then we pushed and pushed to get the next one."
Neil changed formation to 4-4-2, pairing Stockley with Sean Maguire, the width coming from Brad Potts and Scott Sinclair.
The Scot said: "Trying to play through them is really difficult, Forest are set up to hit on the counter, they are second in the league for counter-attacking goals.
"You could argue the penalty was a counter-attacking goal against us.
"They have only won two games when they have had more possession, so we were quite happy to give them a bit of the ball and try and get them out to create space behind them.
"In the main I thought that worked, I thought the better chances fell to us.
"We changed it towards the end because we needed to put fresh impetus into the game and get the tempo up, we got chances off the back of that.
"So we can't really complain about not getting into good areas.
"Giving the first goal away was frustrating but I thought the lads gave it their all, I thought the subs came on and made an impact."
North End are two points outside the top six but face a tough next assignment at in-form Brentford on Wednesday.
"Frustration is the biggest thing at the moment, it is an opportunity missed," said Neil.
"We are still in the hunt, we have three big games left and the next one if going to be really tough, it looks like we will have to go and win it.
"But it was never going to be easy, we knew we would have to go to tough places and win games."