United have enjoyed a turbulent first season under David Moyes following the retirement of Sir Alex Ferguson and sit seventh in the Premier League table.
A 3-0 home defeat by Liverpool last weekend raised the intensity on Moyes, but United provided their fans with a boost after beating Olympiakos 3-0 in midweek to reach the UEFA Champions League quarter-finals.
The Red Devils followed that up with a 2-0 success at West Ham on Saturday, but Fletcher and his team-mates are not getting carried away by the week's results.
"The team don't like what's happening this season," Fletcher told the Sunday Times.
"The biggest thing, and I felt it, there's been no real celebration since Olympiakos. No, 'Wow, we're back'. There's a lot of work to do. At the end of the game it was, 'Listen lads, we've done nothing'.
"We're in the Champions League but our league position doesn't give us any right to make out we're back."
On a personal level, Fletcher has made 12 appearances for United this season since returning against Aston Villa in December after almost 12 months out of action.
The Scotland international was sidelined due to ulcerative colitis and the 30-year-old has been pleased with his form since making his comeback.
He added: "I'm getting there. I'm feeling stronger and fitter all the time.
"I don't want this to sound cocky, but I've actually surprised myself in the few games I've played, how well I've done.
"I'm the same as any player who hasn't played for 18 months and missed the last three pre-seasons. I can't wait for this pre-season.
"I'm going to train hard all summer. I have good weights and dietary programmes to get my strength back.
"David Moyes has been great but I feel like I'm starting my career again, like I'm 19, coming into the team, new manager. Every little opportunity, every training session I have to prove what I can do."