The Lilywhites were four minutes away from the third round tie going to penalties when the Bluebirds got their winner.
Mark Harris scored for the hosts to make it 2-1 in the 116th minute.
Cardiff had taken a first-half lead through Isaak Davies before Daniel Johnson equalised from the penalty spot nine minutes into the second half.
But defensive errors let in the Welsh side for the winner and they were to later land Liverpool at Anfield in the fourth round draw.
Lowe said: "In the first half we had a lot of good spells. The decision making wasn't as sharp as I would have liked it in terms of breaking the lines and penetrating - getting forward we didn't quite have that.
"In terms of their application and effort, the lads tried their hardest to get through.
"It's disappointing we didn't get through extra-time, at 1-1 we should have taken it through to penalties but a lack of concentration cost us.
"There was a long ball, the type of ball we had dealt with well a lot.
"It was one which we could have headed back or headed out for a throw but we headed it back into the pack, they jumped on it and they counter-attacked us.
"We wanted to win, we wanted to go through to the next round."
Lowe made four changes to the starting XI for the visit to South Wales, one enforced with Andrew Hughes having a slight injury.
Greg Cunningham, Ali McCann, Ryan Ledson and Sean Maguire came into the side.
Later on, there was a substitute appearance for Josh Harrop, his first game for PNE since Boxing Day 2020.
Lowe said: "I needed to look at the squad, we have a big enough squad to be looking at.
"We made a couple of changes to freshen things up a bit and give people an opportunity. The lads who came in did okay.
"There are parts of our football which we need to be a bit more tidy with."
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