But for all their pressure the hosts could not find a winner in the second half, with Plymouth stopper Romain Larrieu pulling off a succession of fine saves.
"We did enough to win the game," Irvine said. "There were an awful lot of attempts on goal, over 40 crosses and I don't know how many corners.
"But a combination of us not being clinical enough in front of goal, them defending really well to their credit and the goalkeeper being outstanding, it stopped us from winning a game we should have won.
"I thought we had got it. It wasn't for the want of trying.
"For periods of the game we were very good, we just didn't convert pressure and the chances into goals we needed.
"We are going along and winning as many points as we possibly can. It would probably be a bit unrealistic to think about the top two from where we have been.
"I was quite happy with a point at the weekend (when Preston drew 0-0 with Sheffield United) because we had to dig very deep for that, but I am bitterly disappointed tonight."
Preston have now gone eight games at home without defeat, but that run had been in danger when Plymouth took a shock lead,
Paul Gallagher's corner came off Preston defender Youl Mawene before Mackie fired home from inside the six-yard box.
Preston drew level before the break when Ross Wallace pumped a long pass forward and Parkin knocked the ball home.
Parkin might have had a hat-trick but for the heroics of Larrieu, who turned one effort on to the right post in added time.
But manager Paul Sturrock was pleased his team had finally scored an away goal, having gone six games without a goal on the road in the league.
He said: "There aren't going to be many teams coming here who will get anything against a side like Preston.
"Getting that away goal has been like a monkey on our shoulders. We have hit the bar, had efforts cleared off the line and goals disallowed.
"It was nice to just get one tonight and hopefully we will just kick on now.
"We have to go and do the business at home now. If we start getting wins at home we'll climb up the table."
Sturrock also had words of praise for goalscorer Mackie, saying he had "a great engine" and was a "handful".
He added: "The last two pairs of centre-backs he has played against will swear by that. He certainly puts himself about."
On his goalkeeper Larrieu, Sturrock said: "He has been in that form since coming back into the team.
"We have stuck by him and he has repaid us tenfold. He is a top quality goalkeeper, 32 now, and he is just maturing as a goalkeeper as well."
There was some bad news for Plymouth, though, with defender David McNamee taken to hospital after being stretched off with a cheekbone injury.