Near silence greeted the final whistle as the 2-1 third-round loss ended United's hopes of silverware while some boos rang out as the players trudged off the pitch.
Former United midfielder Fletcher stepped up from his role as the club's Under-18s coach to take charge of the first team after the sacking of Ruben Amorim last week.
But after a 2-2 draw away to Burnley in the Premier League, his hopes of providing a boost at Old Trafford were frustrated as former United player Danny Welbeck scored for the visitors after Brajan Gruda put them in front early on.
"It was mixed really, we started okay but the goal knocked the stuffing out of us," Fletcher said. "Our passing was quite slow so I challenged them at halftime. It was similar to the game in the week, we needed to move the ball with more tempo.
"When we got back to 2-1, I thought here we go, the crowd was up, the energy was up, but ultimately we couldn't get the equaliser. I think you can see the players are fragile and need to build themselves up. It's up to them to respond."
United are expected to announce a caretaker manager for the rest of the season next week but Fletcher said that whoever that is, it is up to the players to dig deep.
"Confidence is the most powerful thing in football, but when you don't have it you have to dig deep, battle, grind and work and work to win games, then the confidence comes back."
United have failed to survive a round in either of the domestic cup competitions for the first time since 1981-82 and with no European football, the season threatens to fizzle out.
They are seventh in the Premier League, however, and only a point behind fifth place which is likely to be a Champions League qualification spot.
"They are experienced players. They've got to make sure they have a lot to play for this season," he said. "This team is still good enough to achieve success this season but they have to dig deep."
Fletcher was critical of referee Simon Hooper for showing teenager Shea Lacey a second yellow card for hurling the ball down in frustration near the end.
"Shea Lacey's yellow card is ridiculous compared to the fouls that we had against us all game, which ultimately then the lad makes a mistake and is sent off," Fletcher said.
"For me it is poor refereeing."
