A seething Sir Alex Ferguson lashed out at former captain Roy Keane after seeing his side consigned to a humiliating group-stage exit.
United's 2-1 defeat at St Jakob-Park meant they fell at the group phase for the first time in six years and prompted criticism from Keane, analysing the match for ITV, who said that United had "got what they deserved".
His remarks drew 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," said Ferguson 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."
Ferguson was also unable to hide his displeasure at the prospect of a Europa League campaign, despite it raising the possibility of a clash with Manchester City, who also went out of the Champions League on Wednesday.
United's fans have taunted rivals Liverpool for having had to compete in Europe's second-tier tournament in the past and Ferguson showed little enthusiasm for a competition that is sure to drain his squad's resources.
"It's a competition I've never been in with United," he said.
"It does mean one thing. Thursdays all the way through. Thursday and Sundays. That's got to be dealt with. It's not the best, but that's our penalty for not qualifying tonight."
Needing just a point to qualify, United had started in assured fashion but they were rocked in the ninth minute when Basel skipper Marco Streller turned in the opener from Xherdan Shaqiri's left-wing cross.
The visitors came close to an equaliser on several occasions, most notably when Basel defender Markus Steinhofer volleyed against his own crossbar, before Alexander Frei made the game safe with an 84th-minute header.
Phil Jones scrambled home for United with a minute to play but for once United's injury-time onslaught proved fruitless and Ferguson was left to rue the disappearance of his side's cutting edge.
"It wasn't a good start to the game," he said.
"That was a surprise, as we expect to control the game by possession and they scored from their first attack.
"When you're 1-0 down away from home, you have a job to do. We didn't take our opportunities and that was the story of the game."
Ferguson's disappointment was compounded by a knee injury sustained by captain Nemanja Vidic that saw him stretchered off shortly before half-time.
"We don't know at this moment in time," said Ferguson when asked about the severity of the injury.
"We think it's the medial ligament. Hopefully that's the worst of it."
As last season's beaten finalists wallowed in the misery of one of their most damaging defeats in recent memory, Basel were left to reflect on a win that opened up the door to the last 16 for the first time since 2002-03.
"What can I say? I'm very proud," said Heiko Vogel, who was appointed Basel coach in October after Thorsten Fink left for Hamburg.
"Tactically, mentally, physically -- everything worked right. I'll leave the superlatives to you (the media). I think we deserved the victory. I'm beaming with pride."
The Swiss champions now fact the prospect of a last-16 tie against one of the tournament's heavyweights, with holders Barcelona, Real Madrid, Bayern Munich, Inter Milan, Arsenal and Chelsea all potential opponents.
Vogel, though, said he would simply try to enjoy the moment.
"No," he replied when asked if he had a preferred opponent. "Whoever comes, can come."