Elliott netted both of the Young Lions' goals in the semi-final victory, the second coming just four minutes from time.
He now has three knockout goals in Slovakia and heads into Saturday's final looking for back-to-back titles, alongside coach Carsley and Charlie Cresswell.
Speaking about his match winner, Carsley said to reporters after the contest: "I thought he was outstanding. I think he has grown as the tournament has gone on.
"I think he was definitely frustrated at the last tournament with the amount of game time that he had but the players he was competing with, him and Charlie (Cresswell), they had to be patient and they showed during the qualifying campaign they were ready to lead and carry the team on along with the other players.
"But Harvey is getting stronger as the tournament is growing, he’s a threat in front of goal, which we always knew, he’s definitely got assists in his arsenal too, and hopefully he can continue that into the final."
For the winger, it was another coming-of-age moment as his name was sung around the National Football Stadium in the Slovak capital alongside his player of the match trophy - his second in the tournament.
Asked whether he is the man for the big occasion, Elliott told reporters in the mixed zone: "I’m trying. It’s a situation where I kind of know what it takes to be in the end stage of these tournaments.
"I’ve been here before, and I’ve seen players do it before where they’ve had to step up, especially when times are tough and our backs are against the wall.
"It’s about how you dig deep, how you keep going and fight till the very end. To be able to contribute two goals and win the game, I’m proper made up.
"It’s one of them where we have a final to worry about, we can’t get too carried away, we need to recover, rest and go again."
There was some slight concern after the game when Elliott said to British broadcaster Channel 4 that he had hurt his knee during the celebrations of his first goal, but he walked past the media without any issues.
He added: "The pitch was drying out towards the end, and it’s one of those where, in the moment, the emotions get the better of you.
"I remember looking down at my sock, and it was ripped because of how dry it was. It’s something that hopefully isn’t a problem."
Carsley's side's only big moment of panic was Noah Ohio's 45-yard leveller with 17 minutes to go, but the manager was proud of how his team responded.
"They responded really well. We were pretty much in control at that point. We always talk about that 'domino effect' of making one mistake and then two mistakes, and the lad (Ohio) took the goal really well.
"It's obviously something that he's seen that could potentially be on if they win the ball in that area.
"We're obviously disappointed to concede that goal because we have gone from being in a really good attacking position to giving them that chance.
"...It was almost instantly that they recovered from the mistake, and they deserve a lot of credit."