June Steenkamp told British broadcaster ITV that she was "settled" with Pistorius's sentence for killing Reeva Steenkamp, even though it could mean he is out of prison and under house arrest after 10 months.
Looking pale and holding her husband Barry's hand, she added: "We don't want revenge, we want a fair punishment under the circumstances on his disabilities.
"We wouldn't have wanted him to go to jail and be abused and I feel that he will realise that he can't go around doing that, he can't kill someone like that."
Pistorius, 27, had testified that he shot the 29-year-old model four times through a locked bathroom door at his Pretoria home after he mistakenly believed she was an intruder.
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Prosecutors had argued that he murdered her in a fit of rage after an argument in the early hours of Valentine's Day last year.
June Steenkamp reacted angrily in September when he was acquitted of the murder charge.
"There is still something missing," her husband, Barry Steenkamp, said at the time. "I think there was more to the whole story, you know, coming up to the actual shooting, the killing."
But in the interview aired today, June Steenkamp said the family had accepted the judge's decision, despite indicating that some members were not "entirely happy".
"We're very settled with the sentence," she added.
"He has go to pay for what he has done and it is not that we want vengeance or anything, or for him to suffer with his disabilities.
"If there is an appeal, well, there is an appeal. There is nothing we can change about that but it will be difficult to go on even further, again."
Steenkamp said: "We will see her again one day when we are in the same place but still there is a great, great empty space for us and it is very hard.