"That's what we want, win the game. At the end of the season we'll see if we fight for the title," Jesus said after the game.
"This season is a difficult season for everyone. We cannot drop at home. We did not drop and won the game.
"It's important [to end his goal drought]. To play for a top club I have to score. Today we didn't have the space to play. I have the first chance, I scored and that's good for me and the team."
Poor defending from Sheffield United gave City the opportunity to score after just nine minutes.
Ferran Torres, despite falling over, ducked and dived away from his marker in the box before cutting the ball in to Jesus who tapped home from the six-yard box.
The goal breaks Jesus' nine-game Premier League scoreless streak with his last strike coming vs. Liverpool on Nov. 8.
"We said this will be one of the toughest games of the season and it was," City manager Pep Guardiola said after the game.
"The weather is the same for both sides. It's so difficult because they defend with 10 players. Their team have been together a long time so they know what to do.
"We started good. We maintained it in the second half. We struggled because they are a very good side. They are alive, you can feel it. They shout, they talk, they stick together until the end."