The Brazilian striker's impressive night in the semi-final first leg at the Etihad Stadium takes his tally up to 12 goals in 26 games in all competitions this season.
It is the first time in his professional career that the 21-year-old has netted four times in a single game and he hopes it leads to more regular appearances in the starting XI.
"I have never scored four before in my career; I am so happy for this," Jesus told Sky Sports. "We played very well and with respect to Burton, that's important.
"Players like me want to play more, to help the team, and we went out there to win."
He continued to City's website: "I am so happy because last year I didn't score a lot so that is difficult because I am a striker and I need to score.
"I work very hard every day to play when I have the chance to play for City. I work hard and play well, so I'm so happy tonight."
On Tuesday, coach Pep Guardiola challenged the striker to step up the fight to dislodge Sergio Aguero from his place as first-choice striker.
In the wake of his star performance against the League One side, Guardiola was asked if it would help his chances of cementing a spot in the team.
"A striker needs goals,” he said at his post-game press conference. "He had chances last game and today he scored.
"It’ll be good for him, good for the team, good for everybody!"
City's are in action again on Monday when they host Wolves in the Premier League, followed by a visit to Huddersfield. The second leg against Burton will take place on January 23.