Ferguson's blast came after Suarez's refusal to to shake Patrice Evra's hand ahead of Saturday's Premier League clash at Old Trafford.
The Red Devils captain offered his hand to the Uruguay international, who was banned for eight matches for racially abusing the defender, but he bypassed the Frenchman and went straight to goalkeeper David de Gea.
Evra did not accept that and attempted to grab Suarez's arm to complete the formalities, but the striker shrugged him off.
Both sets of players reportedly clashed in the tunnel at half-time and again on the pitch as United celebrated their 2-1 victory.
On Suarez's refusal to shake Evra's hand, Ferguson said: "I could not believe it, I just could not believe it.
"He's a disgrace to Liverpool Football Club, that certain player should not be allowed to play for Liverpool again.
"The history that club's got and he does that and in a situation like today could have caused a riot.
"I was really disappointed in that guy, it was terrible what he did."
Ferguson added on Sky Sports 2: "It created a tension, you've seen the referee didn't know what to do about it.
"It caught him off guard. It was a terrible start to the game, a terrible atmosphere it created."
Asked if the pre-match handshakes should have been scrapped for the game as it was last month when John Terry and Anton Ferdinand faced each other, he said: "That's a different issue altogether.
"It's never been a problem really up until this situation regarding racism, it's never been a problem.
"We've got to get our house in order in terms of fighting racism. It's an important issue in this country.
"Football's come a long way from the days of John Barnes when they were throwing bananas at him to where we are today. We can't go back. We have to go forward in a positive way and ban it altogether."
Evra enthusiastically celebrated the win in front of Suarez at the end.
"He shouldn't have done that," Ferguson said.
Rio Ferdinand, who was next in line to De Gea at the pre-match handshakes, refused to shake Suarez's hand.
Liverpool boss Kenny Dalglish launched a furious defence of his player following the match.
The Scot, who has backed his player throughout the whole saga, told Sky Sports 2: "I never knew he never shook his hand.
"I don't know, I wasn't there, I never saw it. We haven't looked at the handshakes, but that's contrary to what I was told."
When told Suarez had refused to shake Evra's hand, he added: "We'll ask him and we'll take it from there."
When pressed further by tunnel interviewer Geoff Shreeves whether he would have to look seriously at the refusal to shake hands in light of the confrontations that followed at half-time and full-time, Dalglish said: "I think you're very severe and I think you're bang out of order to blame Luis Suarez for anything that happened here today.
"I think predominantly both sets of fans behaved really well, they had a bit of banter between each other, no problem. How many bookings were there?"
Wayne Rooney, who scored twice for United, was unwilling to get involved in the row.
When asked about it he told Sky Sports 2: "We are all professionals, we have to go and do our jobs on the pitch. We have to concentrate on that.
"I think that's between the two individuals, it's not for us to get involved in."
Evra, as United captain, had led out the side, and as Suarez, playing his first match since returning from his ban, emerged from the tunnel next to last in Liverpool's line-up he was immediately booed.
The Premier League had deemed there was no reason to cancel the handshakes, as they had done between QPR and Chelsea last month in an effort to ease tensions due to Terry's charge of racially abusing Rangers defender Ferdinand, an allegation the Chelsea captain denies.
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