Despite falling behind to James Maddison's deflected free kick, United levelled the scoreline through Yoshinori Mutō's first goal at St. James' Park but the Magpies were unable to progress to round three after suffering a 4-2 loss via spot kicks.
Jonjo Shelvey and Isaac Hayden both saw their attempts saved by Kasper Schmeichel, either side of United goalkeeper Karl Darlow denying Harvey Barnes from 12 yards and Longstaff, who played the full 90 minutes in his first-team debut for the Magpies, felt his side deserved more from the cup tie.
The 19-year-old told nufc.co.uk: "I thought we defended well, especially in the first half. Nothing could be done about the goal we conceded. He (Maddison) has hit the free kick and it took a deflection and those things happens sometimes but other than that, I don't think they had many chances. We had a few attacks and another time they may have come to something.
"I thought we reacted pretty well and stayed solid and took the chance we took. In the second half, we scored a good goal and from there, we had a few half chances. We got a lot of momentum when we equalise and on other day, we probably could have taken the half chances that we had.
"I felt I should have shot a couple of times around the box but you learn from that and as a team it's unlucky to lose on penalties.
"It's all about luck. Someone has to miss and it's unlucky but I thought we put up a good fight and we were unfortunate to go out that way. There will be good and bad bits to take from the game but, overall, it is disappointing to lose."
A product of Newcastle's Academy, Longstaff reflected positively on making his first-team debut for his boyhood club with the Newcastle-born teenager coming up against a strong Leicester side containing former Magpie Ayoze Pérez, Jamie Vardy and James Maddison.
Longstaff, who scored the winning goal in United's 2-1 friendly win against AS Saint-Étienne, believes the experienced gained from the second round clash can heavily benefit him in the early stages of his playing career.
He added: "I thought the fans were great and you get a real buzz when you get to play here. To make my first competitive game for Newcastle is always good. Obviously I would have liked to go out and win it but it's one of those things where I've got the experience now and playing against a top team in Leicester.
"It's a good learning curve for me and shows where I can improve and try to get to the top level. Going up against those players can only help and develop myself. They put out a strong team and we managed to cope well.
"At 19 years old, it's one of those things where you always hope it will happen one day and luckily it happened. It gives you that edge to go and want more and get playing time. I'll always remember this one."
Newcastle turn their attention to Premier League action on Saturday as the Magpies host Watford at St. James' Park (kick-off 3pm BST), who are the only top-flight side yet to register a point after their opening three league defeats.
And, after last weekend's brilliant 1-0 win at Tottenham Hotspur, Longstaff is hopeful United can extend their points tally before the upcoming international break.
"I thought we were excellent against Tottenham last week," he said. "We defended very well and limited their chances whilst talking ours.
"We know Watford are going to be ready to go. They haven't had results so they will be coming here trying to get one. I know we'll be ready come Saturday and hopefully we can pick up the three points before the international break.
"Six points from the first four games would be very good. We didn't manage to win a game after ten last season so we've won one early and if we can get another victory, it will be a big momentum for the boys."
