The Australian striker was sent off for a challenge on Kenny Miller during last weekend's 2-0 loss at Fir Park.
McDonald, who had been linked with a move to Western Sydney Wanderers, will be suspended for the two league games against Hearts and Aberdeen.
He told BBC Scotland's Sportscene on Sunday that he was "disappointed" with referee Willie Collum's decision.
The striker added: "I feel I take the ball and my momentum means I can't really do anything but go into Kenny.
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"I go to win the ball, I lunge in, I actually take the ball and, as impact is braced, I've actually bent my leg for impact rather than a straight leg.
"If I straighten my leg then I think Kenny is in a world of trouble, but there's no intent there."
Moments prior to the announcement by the Scottish Football Association's disciplinary panel, Well manager Mark McGhee had said he was "100% convinced it wasn't a red card".
He told reporters at the club's media conference on Thursday: "I'm not 100% convinced the people over there [at Hampden] will see that, or be prepared to turn it over."
Motherwell's appeal against the red card shown to Scott McDonald in the defeat by Rangers has been dismissed.