The manager saw right-back Rafael refuse a handshake after defensive errors led to his substitution, but the Red Devils recovered to win after Wayne Rooney's double and an assist
The Royals first went ahead through Hal Robson-Kanu, fell behind after goals from Anderson and Wayne Rooney, and retook the lead through Adam Le Fondre and Sean Morrison. Rooney struck a penalty and Robin van Persie netted a winner to finish off the scoring.
Commenting on the extraordinary match, Ferguson told BBC Sport: "It was agony, the worst defending this season, without a doubt. To lose three goals in that manner - we've got to do something about that.
"We're having to rescue the situation all the time. Fortunately we've got players who can do that. Wayne today, in the first half, I thought was absolutely magnificent. He and Van Persie and Ashley Young were a threat to them all the time.
"We should have had a fifth goal, I don't know why it wasn't allowed. It was at least a foot over the line. In the second half we had two or three real good opportunities to finish it off. With the nature of that game today, I was just glad to get over the line to be honest with you.
"We need to sort that out, or we'll get battered. We deserved to be battered today. But scoring goals rescues us all the time."
Asked about the character his side displayed to record an eventual victory he told ESPN: "It's not a question of character at all with those boys.
"But if you make mistakes like that defending you’re going to have to do rescue jobs every week. Today again was a rescue job.
"We brought Chris Smalling on, that made a big difference in terms of height defending set pieces, although they didn't get as many in the second half."
Smalling was brought on after just 31 minutes in place of Rafael, who stormed off the pitch and refused Ferguson’s offer of a hand-shake.
Sir Alex did not criticise the 22-year-old right back when asked about his reaction to being substituted, and responded: "That’s nothing, the boy was disappointed at coming off. He's been one of our best players all season."
The result gave the Red Devils a three-point lead over Manchester City who they must face at the Etihad Stadium next weekend, after their rivals could only draw against Everton, and Sir Alex insists they must improve.
"It's going to be a tough game. You know the quality of Manchester City, they're a terrific team. And if we defend like that then... I'll be able to play myself," the manager joked.
Rooney had struck a penalty to put United 2-1 up, before he netted his side's third to draw level after half an hour and set up Robin van Persie's winner with a clever flick.
More drama followed when the Dutch striker had another cleared off the line when replays showed a goal should have been awarded, and later blasted a glaring opportunity over the bar.
Asked if the match was a good one to play in, Rooney commented: "When you look back it is enjoyable but when you're playing you don’t know what’s going to happen and it's end to end - a bit like a basketball match - so it’s quite difficult.
"But I'm sure the fans will be delighted to watch it. It was important to come away from here with the three points regardless of the performance.
"There's always pressure to score on a penalty. I was delighted to score and put us 2-1 up, and although we conceded two more after that we managed to come back quickly.
"Van Persie's goal was a difficult call for the linesman as he struck the ball so hard, but hopefully next time it will go our way."