Jurgen Klopp's men advanced to the fourth round with a 2-0 victory over MK Dons, thanks to goals from James Milner and Ki-Jana Hoever.
Elliott played the full 90 minutes on the right-hand side of a front three alongside Rhian Brewster and Curtis Jones, impressing with his passing range and composure on the ball.
And Warnock, who played for Liverpool between 2002 and 2007, singled out Elliott for his eye-catching performance post-match.
"[He showed] a maturity way beyond his years," the former Reds defender told Sky Sports.
"Often you see youngsters, 16 years old, and they take too many touches because they're nervous, they want to get the ball under control.
"He's pinging balls in, one-touch and round the corner, clever play.
"I thought his miss last night, when he hit the crossbar early on from so close, might have dented his confidence. It didn't at all.
"This guy is full of confidence and you could see it in his performance, how well he did. Very unfortunate not to score late on, he can be delighted with his performance."
Hoever, Brewster, Jones and goalkeeper Caoimhin Kelleher also played the full match at Stadium MK, with Klopp content to blood the younger members of his squad in the domestic competition.
Warnock feels the academy graduates have already taken on board Klopp's unique philosophy, as he added: "They all try and play in a similar way.
"If you are going to progress into Jurgen Klopp's team, you need to be able to play in the positions that he has on the pitch - whether that be in the front three, the midfield three or the back four.
"You've got to understand what he's looking for, and that will be filtered down to the academy staff from Jurgen Klopp. That is massively important.
"Last night when the players were on the pitch you could see they understood what the rotations were, defensively what they had to do.
"That is part of the blueprint that Jurgen Klopp is passing down to the academy."