However, with his own interest at an end, the former England skipper wants United to reclaim a trophy he helped them win in 1999.
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"I really hope they go all the way."
With Real Madrid out of the Champions League, United have an excellent chance of reaching their third successive final.
And Beckham will have a scarf to wear as well after wrapping himself in green and gold as he made his way off the field.
The colours of Newton Heath have become the focal point of a growing anti-Glazer campaign, aimed at ousting United's owners.
Just by wearing the scarf, Beckham has ensured massive publicity for the green and gold campaign, although he denied it was his own attempt to register a protest.
"I'm a Man United fan. I saw the scarf there. I put it round my neck, it's the old colours of Man United, that's all I knew," he said.
"To be honest it's (the protest) not my business. I'm a Manchester United fan. I support the club. I always have done and I always will do. It's nothing to do with me the way everything is run, that's to do with other people but I'm a Man United fan and I support the team. I will always support them."
Beckham admitted he was aware of the gathering protests against United's owners, adding: "Obviously you can hear it week in and week out. There's always protests going on. Let's hope it gets sorted out."
Although Park Ji-sung and Darren Fletcher wrapped up victory, Beckham's England team-mate Wayne Rooney did the damage last night.
Rooney scored at the start of both halves to kill off the tie, which United won 7-2 on aggregate, to take his tally for the season to 30, just 12 short of the amazing number Cristiano Ronaldo recorded two seasons ago.
"His performance was a continuation of his form in the last few months - just sensational and unbelievable," said Sir Alex Ferguson.
United would have expected to be lined up against Ronaldo in the quarter-final draw next Friday.
Instead, Real were dumped out of the competition by Lyon, who joined Arsenal, United and Bayern Munich as the quartet who are definitely through to the last eight.
"I was surprised at Real Madrid's result," said Ferguson.
"But European football is very tough now. In the last few years English clubs have done very well and I think they will be there again.
"It doesn't matter who we play in the quarters. We are there and hopefully we take advantage."