William Gallas, whose own goal had given United a first-half lead, volleyed an injury-time equaliser for the Gunners.
"I think Howard Webb has a great chance to be the top referee but today was a big game for him and, at times, he favoured Arsenal," Ferguson told MUTV.
"Their second goal came from him not giving a free-kick for a foul on Louis Saha on the far side. It should have been a foul for us."
Ferguson believes it can be difficult for referees not to be influenced by hostile home crowds.
"It is very difficult for the referee," he said. "On our bench, we were getting terrible abuse from people two or three feet away from us.
"There is a lack of security here. It is absolutely disgraceful the abuse you and your staff take. All sorts of things are been shouted and screamed at you and there is an absolute danger here."
He said: "I think we have thrown it away. At 2-1 you think you've won the game and for them to get a second goal when they did - for us to give it way in injury-time - it is very hard to take I can tell you. It is a fact that they got out of jail.
"We spoke about it at half-time, the importance of not letting them back in and we started the second half well and then we lose a goal from having our own throw in near their corner flag. It's amazing. It's criminal.
"After their equaliser, Arsenal got at us for five or 10 minutes but then it seemed to be heading for a draw.
"I don't settle for a point at any time. We send a team out with ability to win matches and we try to win matches.
"We settled quite well after their equaliser and Wayne Rooney had a marvellous chance. Some of our attacking play was great, some of our football was threatening.
"In a game of that magnitude, there was going to be chances. We had ours and they had theirs."
Ferguson felt Arsenal, who have reached the top of the table by playing attractive football, had resorted to direct tactics to force their way back into the game.
He said: "Arsenal are good football team and they had plenty of possession but they didn't actually make anything of their chances.
"They got their second goal from pumping the ball into the box. It got a bit of a deflection when they pumped the ball into the box in injury-time and ended up at the back post (with Gallas). I think it (Gallas' volley) was over the line. Edwin (van der Sar) thought it was over the line.
"We produced some good football for our goals but their goals were a bit scrappy. It's unlike Arsenal. They normally score goals from good passing movements. Today they were slashing the ball in the box and getting goals from it."
A relieved Wenger said: "The referee interrupted the game and I thought he had given a free-kick against us for offside, so I had a surprise because the ball was in.
"It was fantastic for the linesman because he was on the wrong side. He saw it, I don't know how but when you see it on television the ball was in by a yard.
"I've not to thank him. He did his job well. I congratulate him but don't thank him. He did the job like you expect him to do it."
He added: "Our character was tested twice. We were down and came back against a very good Manchester United side. They looked as if they could always take advantage of any mistake we made.
"They have clinical players and they did that well but they didn't create a lot. Overall it was a fair result.
"In the first half we played with the handbrake on and in the second half had more freedom but we didn't find our flowing game completely. We had to rely on character and determination.
"We were tentative and too cautious. We played at the wrong pace and allowed United to control us quite well, sharpness-wise we were not at our best but character-wise we have shown plenty again.
"There is something special in this side which you don't see at first because it attracts you more with technical ability. There is some resilience and character which is well hidden."