Dunfermline were originally thrown out the cup for breaching rules, including fielding an ineligible player.
But SFA chief executive Gordon Smith does not think the cup's reputation has been damaged as the decision was taken by an independent panel.
Smith had been part of an emergency committee that last week kicked the Pars out the cup after they admitted a number of rule breaches during their 7-1 win at East End Park.
The Fife club on Thursday won their appeal against that punishment but were ordered to replay their fourth-round tie with Stenhousemuir - but at their opponents' ground - and were fined about £30,000.
I have to stand by the fact that an appeals board have the right to look at all the evidence
Scottish FA chief executive Gordon Smith
Smith said at the time of the original decision that the "integrity" of the competition was paramount in the emergency committee's unanimous ruling.
"If you set down regulations and rules, you expect clubs to abide by them," said the SFA chief.
"Depending on how many rules are broken, you could say the cup could be damaged by that.
"That's why I made that statement. But, in regard to the cup, I don't think it's compromised.
"The club have been put back into it and we just have to accept that that is the decision.
"The integrity of the cup hasn't been compromised because an independent board decided to allow Stenhousemuir and Dunfermline to play again."
Smith said he was personally opposed to the appeal panel's decision and said he could understand Stenhousemuir's anger at possibly being denied a lucrative fifth-round tie against Celtic.
"Very few appeals are won - most of the time the original decision has been regarded as being the correct one," he said.
"I was quite surprised that the decision we had made was not regarded in that light.
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"But I have to stand by the fact that an appeals board have the right to look at all the evidence."
Meanwhile, Dunfermline manager Jim McIntyre was relieved that his side have been given a reprieve.
"All we asked for was a fair hearing and we got that," he said. "We are delighted with the decision that gives us a chance to progress in the competition - that's all we ever wanted.
"We know that we broke the rules and we have publicly apologised for that.
"Now we are back in the competition, it is up to us. We have to start all over again with the right attitude and try to get the right result to take us through to the next round.
"That is a big carrot for both teams. No two games are the same and one thing that's for sure is that Stenny will be much better than they were the first time round."
Source: BBC Sport
Source: BBC Sport