The comments came following Suarez's refusal to to shake Patrice Evra's hand ahead of the Barclays 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 [Saturday] 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 [Saturday]. 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.
"I was disappointed it's ended up 2-1," Ferguson told Sky Sports 2.
"Maybe we did tend to just try and play out the game, keep possession and not really threaten in the way we did before we got the goal.
"That's the only fault I can find with the players because right through the team they played some fantastic football."
United might have taken the lead in the first half, but Paul Scholes' header was well saved by goalkeeper Jose Reina.
Ferguson added: "I thought Danny Welbeck was terrific, particularly in the first half. Scholesy was unlucky with his header, the goalkeeper had a good save.
"I thought we were really well on top of the game. It's just getting that goal and of course Wayne has scored and then two minutes later scored another one which was a great start to the second half for us."
Suarez halved the deficit 10 minutes from time and Ferguson admitted it was a nervous wait for the final whistle.
"Oh crikey me, I think my heart's still out there," he said.
"It was nervy in the sense you were playing Liverpool and they've come back from 2-0 down to 2-1 and you know football, anything can happen."
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.''