There was no disgrace in losing 4-1 on aggregate to the reigning champions of Europe in the semi-finals but Arsenal, who are fourth in the Premier League, have now failed to win a trophy for a fourth successive season.
Togo striker Adebayor, widely criticised for his recent performances, said afterwards their trophy drought had lasted too long and the north London club must do everything they can to end their barren spell next season.
"It has been a long time without a trophy. I joined in 2006 and I feel sorry for not winning anything in three years," Adebayor told Sky Sports News.
"Now for next season I don't know how we are going to do to be honest. I don't know how we are going to manage.
"What we are going to try to do is score with our head, our toes, whatever. We just have to try and bring trophies to this club."
Whether Adebayor will still be there is debatable, as is manager Arsene Wenger's policy of buying young untried players and moulding them into a championship or trophy-winning side.
With an average age of 23, compared to United's 27, it appeared to United defender Patrice Evra "that it was men against boys out there," as he said afterwards.
Arsenal's teenage prospect Kieran Gibbs, at 19 the youngest in the team, made the mistake that led to United's opening goal from Park Ji-sung after eight minutes and was so distraught at halftime that Wenger replaced him with Emmanuel Eboue.
United wrapped up the tie after just 11 minutes when Cesc Fabregas, Arsenal's 22-year-old skipper, gave the ball away to Cristiano Ronaldo who was fouled by Robin van Persie and scored from the ensuing 40-metre free-kick.
Fabregas is Arsenal's outstanding talent and one of the best young players in Europe but without the injured William Gallas, or experienced campaigners like the long-departed Tony Adams or Patrick Vieira, they lack an authoritative leader on the field.
