The Red Devils conceded a goal in the ninth minute when Marco Strellar knocked the ball into the net after goalkeeper David De Gea failed to clear the uncontested cross from Xherdan Shaqiri.
The score would remain 1-0 until the 84th minute. Alexander Frei headed the ball in from three yards out to give Basel the cushion. Phil Jones cut the lead in half in the 89th minute, but United couldn't manage a miracle second goal before the final whistle.
To add injury to insult, Nemanja Vidic suffered a knee injury minutes before half time.
Manchester United were the aggressor in the match, but simply couldn't execute. The Red Devils took 22 shots, with six on goal, while Basel took 12 shots, with five on goal. United had possession for 57 percent of the match.
This is a major blow to Sir Alex Ferguson. The loss means Manchester United have failed to advance to the knockout stages for only the third time in 17 years.
The win puts Basel into the Round of 16 for the second time in the club's history.
Here are highlights from the first half: