Preston boss happy to progress in cup after shoot-out win over Hull City
Paul Huntington and Josh Harrop had puts the hosts 2-0 up after only 25 minutes, but John Magennis pulled a goal back from the penalty spot.
North End then conceded with virtually the last kick of the game when Jarrod Bowen converted from close range to send the game to a shoot-out.
Goalkeeper Connor Ripley was the hero for PNE as he saved Tom Eaves' spot-kick - and it was left to Alan Browne to smash home the winning penalty.
"I thought first half, we were great and thoroughly deserved the 2-0 lead and pobably even more based on the play," Neil said.
"We didn't use the ball well enough, we didn't compete well enough in the second half," said Neil.
"I had a discussion with the players after the 90 minutes. I said, 'Listen we have messed it up so the only way to fix it is to go and win the penalties'.
"I thought they showed good composure after a disappointing end to the game. To lose a goal that late, it's easy to let it affects you.
"I thought they were all brave stood up, stuck the ball away and Connor Ripley makes a very good save for us.
"I think all in all over the 90 minutes, I think we certainly deserved to go through.
"Even in the second half when they had pressure, we had the clearer chances in the game to win comfortably."
Neil revealed that Tom Barkhuizen came off at half-time with a groin problem and is doubtful for this weekend's trip to Nottingham Forest in the Championship.