Last year's runner-up frittered away a 12-9 lead to lose 13-12 in the second round, the 22-year-old title favourite beaten in a Crucible classic which reached its climax in a 46-minute deciding frame.
Carter complained that Trump had all the luck in the match, and was so frustrated when he was put in a snooker behind the brown and yellow balls in the 23rd frame, seemingly by fluke, that he applauded sarcastically.
"If he wants to do that, then it's up to him, but he's 30-odd years old and it's a bit childish," Trump said.
Carter, 32, said the match proved that snooker is about more than simply potting balls.
Trump was baffled by the remark, and said: "I'm still a lot younger than him and have done a lot better, so let's just let the snooker do the talking."
Trump had been 9-7 ahead going into the concluding session of the match and almost made a maximum break in the afternoon's third frame but could not find position on a 13th red.
It put him 11-8 ahead though, and despite Carter taking the next with a 94 break, Trump soon re-established his three-frame cushion.
Carter began to eat into the lead though, and had his own maximum chance but could manage only 81. It put him back at 12-10, then Carter closed the gap further by taking a scrappy frame and drew level aided by a run of 53.
Trump missed a red with the rest to present Carter with a match-winning chance in the decider. He made 47 which left Trump needing four snookers, and remarkably he found three of them.
But Carter, fighting an ongoing battle with Crohn's disease, an inflammatory bowel condition, mopped up the colours he required to claim a hugely satisfying win.
Carter said: "Judd just pots them from everywhere but there's more to this game than potting them from everywhere, believe me. I've proved that today [Monday].
"He had three or four lashes in the last frame like he did the whole match and got away with it. He just did not stop getting away with it the whole time.
"I'm glad today [Monday] that I was strong enough to stand and beat him, but he will be getting beaten in my opinion. It's easy for me to say that now because I've come out the winner but I'm delighted with myself because I've been on the wrong end of too many matches like that.
"Now he can know what it feels like to have a nasty scar in your career and it's not easy to get over. He was in here to win it but so am I."
Carter said there was "no needle" between the pair, but he was happy to say the Bristol youngster has a one-dimensional game.
"Very much so," Carter said.
"He's had a great run, but these last five or six tournaments since (winning) the UK Championship, it's been a little bit different for him.
"Now he's expected to win and blast everyone off the table.
"I know my way around a table as well and I knew how to break him down in the end."
Carter's fightback was not dissimilar in its manner to the way Peter Ebdon came from 8-2 behind to defeat Ronnie O'Sullivan in the quarter-finals seven years ago.
Carter had 2002 world champion Ebdon in the crowd supporting him, which Trump said was "a bit strange".
Trump said: "A lot of players enjoy me losing. 99% of people are on my side and I take no real notice of any other players."
Carter explained Ebdon had given him some pointers on how to win closely-fought matches.
"Peter came up to support me and give me some words of wisdom," Carter said.
"He know what it's like to be world champion. He's been there and done it. I haven't and nor have a lot of players. He's got some invaluable advice for me and I respect Peter.
"It's all very well having these sports psychologists. But they don't know what it's like to be out there playing under pressure. Peter does and that's why I respect him.
"He's just giving me some words of advice and words of wisdom, and telling me a few things that might help in the tight situations, and sometimes any little edge you can get can be enough, like you saw today [Monday].
"At 12-12, Judd missed a red with the rest by a millimetre. He's not gone through the ball quite quick enough on it, flicked a bit of side on, and missed - I've won. That's all it is sometimes."
Carter came into the match stressing that it would only become clear what a player world number two Trump is once he has to fight back from damaging defeats.
This loss was as painful as any he can have experienced, but for Carter it was a result to savour.
Carter said: "In a way it makes it sweeter that I had to suffer for another 10 minutes and get out of snookers and play a bit more. It makes the win all the more sweet."