After claiming an away draw against strongest group rivals Benfica in their opening match a fortnight ago, United already looked well-placed to claim their customary last-16 berth.
Romanian debutants Otelul Galati have to be faced in back-to-back meetings next month, so if Basle are dismissed with customary efficiency at Old Trafford on Tuesday, it is hard to imagine Sir Alex Ferguson's men being stopped.
But Fletcher is acutely aware life is never quite so easy.
It is only two seasons ago that United lost to Besiktas on home soil. And the Scotland skipper is determined to avoid a similar setback.
"You've got to be cautious about unknown quantities," said the 27-year-old.
"Obviously we went to Benfica and got a draw, but the two we face in our next two games are a little bit unknown. Some people expect you to just walk over teams like that and win comfortably.
"It's never as easy as that though.
"We are playing in the Champions League and we from past experience how difficult it is.
"We must have the right attitude and make sure we perform because if we get the three points it would set us up nicely."
Given their form so far this term, United can approach their task with confidence.
Including the Community Shield win over Manchester City, the Red Devils headed into the weekend boasting seven wins from eight fixtures, with only Benfica denying them at the Stadium of Light earlier this month.
United have scored three goals on six occasions, accounting for London giants Tottenham, Arsenal and Chelsea in the process.
Yet Fletcher agrees with his manager's assessment that the season has not been up and running long enough to gain any true picture of how the entire campaign is going to unfold.
"You can see where the manager is coming from," he said. "It is still early days.
"We keep looking back to Chelsea's fantastic start last season. Everyone thought they were going to walk the league, but they didn't."
Instead, it is how United come through the inevitable setback that Fletcher believes will determine their progress.
"You must come through it quickly and respond," he said.
"We are playing well just now but there are improvements to be made. Chelsea created a lot of chances against us last week. Although we won the match, maybe we were a little bit fortunate.
"Whilst we are playing well and winning, you always have to look at your performances and what you can do to improve in the future because ultimately, giving away that number of opportunities will cost us."