Suarez reopened old wounds this week with a scathing attack on the processes which landed him with an eight-match ban and £40,000 (Dh230,600) fine last season.
He accused United of having too much power and said he was reduced to tears when he was found guilty by an FA disciplinary committee.
The Uruguay forward also blamed Evra for the very public failure to shake hands prior to the Old Trafford encounter between the north-west giants, which forced Reds owner John Henry to step in.
Ferguson, though, believes such accusations are misplaced.
"I think Evra expected him not to shake hands," the Scot said.
"He actually said that to the lads. He just felt that he wasn't going to shake his hand. He was embarrassed to put his hand there.
"But there is no doubt Evra put his hand towards him.
"It's Suarez who should be making the effort to do something about it."
Liverpool were widely condemned for their handling of the affair, with Kenny Dalglish heavily criticised.
And Ferguson believes the negative publicity played a part in getting his fellow Scot the sack this summer.
"I wasn't surprised at Kenny leaving," said Ferguson.
"John Henry has obviously looked at that (the Suarez incident) and felt it wasn't handled in the right way.
"It certainly wasn't a nice thing to happen and it must have been part of it."
That row, coupled with the recent court case involving John Terry and Anton Ferdinand, have not painted football in the best light.
There is a feeling more work needs to be done in an effort to stamp the remaining racial tensions out of the game.
Yet Ferguson feels the incidents have obscured what is largely an impressive track record.
"I don't think there is cause to worry about racism in England," he said.
"Since I have been down here we have made great strides forward.
"I don't see any problem with the game in terms of race."
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