North End were well in the game at 1-1 on Tuesday night after Jon Parkin had cancelled out Rob Earnshaw's 51st-minute opener.
However, a terrible defensive mix-up between keeper Andy Lonergan and defender Andrew Davies let in Earnshaw to net a winner for Forest.
The defeat was Preston's ninth on the road in the Championship this season, with Irvine lamenting his side's inability to pick up points away from home.
"I'm very disappointed, exasperated and angry. I don't think I can use many more words than that," he said.
"It was a game we should not have lost and we lost it from two very poor pieces of defending.
"We got ourselves back in and at that point I thought we were the team who looked more likely to go on and win the game.
"I felt most of the game was being played up at their end and I felt fairly comfortable on the sideline.
"We knew how Forest would play and we matched them up. If it wasn't for two bad pieces of defending, which are out of character for us, we would have got a good result here.
"Our away form is pegging us back but I've said before there is not much different between the teams in the Championship and sometimes the thing that tips the balance might be the home advantage."
Forest assistant boss David Kelly was delighted with the win and urged the players to build on a run that has seen them despatch two promotion candidates in Reading and Preston in their last two games.
"It was a really pleasing win," he said.
"Having gone and got a good win at Reading at the weekend it was important that we tried to back it up and I thought we were value for victory.
"They are a good team and Alan has done a good job with them, but it's still only three points and we must take this form on."
Kelly also paid tribute to striker Earnshaw, whose two contrasting goals earned the vital win.
"It was a fantastic ball from Joel Lynch for the first goal and Rob has found a bit of space and finished well.
"For the second he chased a lost cause and he was on the spot, which is what you want from your goalscorers.
"We are really pleased with the way he is doing, he is working extremely hard for the team and his finishes have been very good."