Arsenal manager Arsene Wenger admitted his team's title hopes are now over - but he was happy with their performance at Old Trafford.
'Yes we are out,' he told Sky Sports One.
'We played with quality and spirit, and I'm very proud of our performance. What can you do?
'We had plenty of chances and we were really unlucky not to win.'
Wenger was at a loss to explain the turnaround in the Gunners' season, having been five points clear at the beginning of February, but feels luck has not been on their side.
'The last two months, we have been not very lucky - and you could see that again,' he said.
'It's difficult to find an obvious reason when you see that performance today.'
There have been suggestions the lack of depth and experience in Arsenal's squad has contributed to their downfall, but Wenger believes the players he has can win silverware.
'I believe this team is good enough,' he added.
'We had a dip since March and we need to look at why, but the biggest target is to keep the team together.'
Rio Ferdinand stressed there is more hard work ahead for Manchester United if they are to successfully defend their Barclays Premier League title after they came from behind to beat Arsenal 2-1.
Emmanuel Adebayor opened the scoring just after half-time with what looked like his arm but Cristiano Ronaldo equalised from the spot after William Gallas handled and Owen Hargreaves grabbed the winner with a precision free-kick.
The result put United six points ahead of Chelsea, who play Wigan tomorrow, with Arsenal now surely out of the race a further three points back.
Defender Ferdinand told Sky Sports: 'There are more points to be played for, the title is not handed out yet.
'We have not many times been a goal down at home but we came back. We showed pure grit and determination and a great team ethic.
'We were maybe fortunate with the penalty but in the second half we looked more like scoring.'
Ferdinand admitted confusion in the United defence contributed to Arsenal's goal as Robin van Persie's cross was allowed to fly right across goal for Adebayor to turn in.
'I heard a shout of `keeper', but Edwin (van der Sar) said he didn't say it, so I've left it and it's gone in,' said the defender.
'It was on my head really.'
Hargreaves surprised everyone, including the Gunners' defence, by taking the free-kick instead of Ronaldo, but he insisted he was always first choice.
'That's a good distance for me so I didn't ask him,' he told Sky Sports.
'It was an open game in the first half, too open, the distances were too big and we had to do a lot of running,' he added.
'Arsenal were the better team in the first half but we had chances too. We needed to tighten up and we did.'