United's 3-1 derby loss to City at the Etihad Stadium left them 11 points behind fourth-place Aston Villa in sixth with 11 games remaining.
"Every time you don't win a game it is a damage at this club," Fernandes said. "We know what this club demands and we want to win the games we are involved in.
"We didn't get the three points today but there's still a long way to go. We know it is not everything in our hands because other teams have to lose points but we have to do our job."
Marcus Rashford gave United an unlikely lead eight minutes into the game with a rasping strike measured at 72 miles per hour. His goal came days after he hit back at critics in a column in The Players Tribune and was one of the lone bright spots for United, who had just three shots to City's 27.
The loss amplified the ongoing conversation around manager Erik ten Hag's future, which has only increased since new co-owner Jim Ratcliffe took control of football operations, with changes expected off the pitch.
United have lost 11 of their 27 league matches this campaign, two more than all of last season. The two previous seasons with 12 league losses (2013-14 and 2021-22) led to managerial changes.
United had been unbeaten in their previous 143 league matches when leading at halftime with 123 wins and 20 draws -- an illustrious run they saw end on Sunday.
"Manchester United will have to take their medicine today. Huge question marks for this team and the manager," former United captain Roy Keane said on Sky Sports.
"Standards have dropped. We're almost praising United. They've lost. They used to perform in the big games and compete," he added.
"Now we're sitting here saying they did alright, better shape. They lost 3-1."
Ten Hag pointed to the fact that Rashford and Jonny Evans were playing with injuries on Sunday. United are also missing striker Rasmus Hojlund, who had scored in six successive league games before being sidelined with a muscle injury, and defender Harry Maguire.
"Absolutely they fought, the togetherness and the performance was very good," Ten Hag said. "On another day we could have won this - small margins."
Ten Hag said their 2-1 loss to Fulham a week earlier was more disappointing. United had been unbeaten in five consecutive league games until then.
"This year on we are really progressing and you have to get some points back," he added. "Everyone can beat everyone and things can quickly turn around. Number five (in the league) can also be a position for Champions League so we have to fight for it."
