Aaron Ramsay scored the only goal of the game as United's bid for a 19th Premier League title suffered a blow.
And although Ferguson admitted Arsenal had a good case for their own penalty when Vidic handled in the first half, he felt hard done by.
Close call: Michael Owen (right) shouts for a penalty after a challenge by Arsenal's Gael Clichy (second left)
'It's too big a game not to get the decisions right,' Ferguson told Sky Sports News.
'It balances out in that respect but I think it was difficult to see that one (Vidic's handball) but the one at the end, Clichy knew, he put his hands up in horror.'
Ferguson added: 'Obviously, it gives Chelsea a major chance now and that's what happens when you get these decisions.
'They got one at Old Trafford last season so that's the worry now.
'But in terms of ability - a game at Old Trafford, the supporters will be ready for it - and so will our players.'
The Scot conceded his team had disappointed until Arsenal scored through Aaron Ramsey in the 56th minute.
'After that we dominated and I think we deserved something,' he said. 'I think we didn't use the ball properly but once we lost the goal we were in their half most of the time.'
Let off: Nemanja Vidic (right) appeared to handle the ball in the area but no penalty was awarded
Arsenal striker Robin van Persie claimed his side 'wanted it more' after the Gunners blew the title race wide open.
He said on Sky Sports News of the Vidic incident: 'A clear penalty and in my opinion a straight red.'
Asked what the referee had said to him, he replied: 'At first nothing because he wasn't sure, but I asked him again just after half-time and he said it wasn't a penalty but I'm sure if he sees it again then he will agree with me.
'If that [United's penalty appeal wrongly turned down] is the case then it's 1-1 on that one but in the end I think we played better today. We wanted it more. They played just on the counter-attack so in the end I think a fair result.'
He added: 'It was all about pride today. The fans were great.
'It was up to us to show some dignity and some honour. We did that today so we're very pleased with that.'
Match-winner Ramsey - only in the team because of a thigh injury to captain Cesc Fabregas - urged Arsenal to press on and finish the season on a high.
Deadlock broken: Aaron Ramsey (centre) scores the winning goal against Manchester United
'Our target was just to keep going now until the end of the season, to win all our games and see where we end up from there,' he said.
'We've done the first bit today. We've still got a few more games left so hopefully we can win them as well.'
Arsenal manager Arsene Wenger conceded it would have been easy for Foy to miss Vidic's handball.
He said: 'If it's on purpose maybe a red card, but I really think the referee has not seen this.'
He added: 'Until we scored the goal, we were the dominant team and you could see after that, the desire to protect the lead was stronger than the desire to score.'
Arsenal have fallen out of the title race in recent weeks and Wenger admitted his side have lacked the 'nerve and experience'.
'It's difficult to fault the attitude and sprit of the team but we lack, maybe, under pressure a little bit of nerve and experience.
'We're playing to be as close as we can (to the top). We need to show that we have fighting spirit and discipline.'
Source: Daily Mail
Source: Daily Mail