The Premier League champions have proven inconsistent this term and face their rivals at the Etihad Stadium having failed to win their last three matches in all competitions.
After surrendering a two-goal lead to draw 2-2 at CSKA Moscow in the UEFA Champions League, City slumped to a 2-1 loss at West Ham in the Premier League last weekend and sit six points behind leaders Chelsea.
Manuel Pellegrini's men also saw their defence of the League Cup ended on Wednesday with a surprise 2-0 home defeat against Newcastle United.
City are therefore under pressure to bounce back in the 168th Manchester derby and Hart is aware improvement is required.
"Not everyone is exactly at their peak just now," said the England goalkeeper.
"We just need a few players, myself included, to step up and it [City's confidence] will come back."
City can take heart from the fact they have won five of their last six Premier League encounters with United.
Pellegrini oversaw a 4-1 victory in the corresponding fixture last September and feels another triumph can ease doubts over City's present form.
"The game we played here at the Etihad was in a moment when I was new here, when maybe there were a lot of doubts about the results," said the Chilean.
"But I didn't change in my mind the way we had to play against every team."
City's recent struggles have taken some of the spotlight away from charismatic United manager Louis van Gaal, who is set to get his first taste of the Manchester derby.
After a shaky start to the season, United have gone four matches unbeaten and claimed a morale-boosting 1-1 draw with Chelsea last time out thanks to Robin van Persie's last-gasp leveller.
United's recent record against City may not provide great cause for optimism, but Van Gaal believes his team are capable of bucking the trend.
"That is our goal, to win," he said. "It is possible. We are growing, we are developing ourselves.
"What we have seen of City in the last few matches was not so good. You never know."
Van Gaal confirmed on Friday that he is set to restore Wayne Rooney to his starting XI after the United and England captain completed a three-match suspension.
Antonio Valencia (hamstring) could also return but Radamel Falcao has failed to shake off a knock and joins Jonny Evans (ankle) on the sidelines, while Phil Jones (shin) is doubtful.
City are without influential playmaker David Silva due to a knee injury sustained against Newcastle.
Frank Lampard (thigh) is another absent midfielder, but Yaya Toure should play despite a groin complaint.
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