United, the European champions in 1968, 1999 and 2008, slumped to a shock 2-1 defeat to Basel FC. The result allowed the Swiss champions to go through from Group C with Benfica.
Meanwhile, City defeated Group A winners Bayern Munich 2-0 but lost out on a last-16 spot when Napoli saw off pointless Villarreal 2-0 in Spain.
It was only the third time in 16 years that Sir Alex Ferguson’s United had crashed at the group phase with Wednesday’s loss coming six years to the day since they last bade farewell at the first round, following a 2-1 loss at Benfica.
Despite needing just a point to go through, last year’s beaten finalists were undone by goals in each half from Marco Streller and Alexander Frei which condemned Ferguson’s side to their first away defeat in the opening round in five years.
Phil Jones’ late goal gave them a glimmer of hope but Basel fought hard in the closing stages to book their place in the last 16 for the first time since 2002-03.
For United, who have played in three of the past four finals, there is now the unwelcome consolation of the Europa League.
“Of course we’re disappointed, there’s no other way you can feel,” Ferguson said.
“It’s part of football. You have to deal with the disappointment, and this club has used it as motivation many times.”
The result drew criticism from Roy Keane, a former United captain now analysing the match for ITV, who said that United had “got what they deserved”. His remarks prompted a stinking rebuke from Ferguson, who was quick to point his finger at Keane’s own less than stellar managerial career.
“I don’t know why you bring up a TV critic,” Ferguson said during a terse post-match press conference. “That’s nothing to do with it. Roy had an opportunity to prove himself as a manager too. It’s not an easy job. We’ve got young players.”
In a double dose of Mancunian misery, City also exited the tournament despite David Silva and Yaya Toure giving them a 2-0 win over a Bayern Munich side weakened by a dose of flu which had spread through the German squad.
Premier League leaders City went into the match knowing the only way they could progress was to beat Bayern, who had already finished top of Group A, and for Napoli to fail to beat Villarreal.
Silva opened the scoring shortly before half-time at Eastlands and Toure scored a second just after the start of the second period.
But Napoli’s 2-0 victory in Spain means Roberto Mancini’s team will now have to combine their push for the Premier League title with a place in the Europa League.
“Usually, with 10 points all the teams go through, always, 99 per cent,” Mancini said.