The Australian striker was sent off for a challenge on Kenny Miller after 27 minutes at Fir Park with the scores tied at 0-0 and Rangers down to 10 men after Michael O'Halloran's red card.
Motherwell's stance was confirmed by the assistant manager James McFadden.
It means McDonald will be free to play against Ross County in the Scottish Premiership on Tuesday.
McDonald told BBC Scotland's Sportscene on Sunday: "Referee Willie Collum's quite far away, but he calls it as he sees it and he gives me a red card.
"I am disappointed with it. I feel I take the ball and my momentum means I can't really do anything but go into Kenny.
"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."
McDonald pointed to a similar challenge by Rob Kiernan on Steve Hammell for which the Rangers defender was booked shortly after O'Halloran's dismissal and before the Well striker was sent off.
"It's a yellow card and I think mine's a yellow card as well," he added.
His opinion of how he caught Miller on the ankle was backed up by McFadden.
"He didn't go in to harm Kenny Miller, he goes in to win the ball and he actually pulls out of it a wee bit," he said.
"The contact happens so fast and they are so close together that we feel it was undeserved."
Motherwell are to appeal against the red card shown to Scott McDonald in Saturday's 2-0 defeat by Rangers.