The Ibrox club's recently-published accounts revealed McCoist earned a salary of £825,000 before agreeing to an unspecified cut.
Rangers ran at a £14.4m loss over a 13-month period until the end of June, and some supporters contacted local media to point out that several players agreed wage cuts soon after the 'oldco' club entered administration in February 2012.
But Smith, the former manager who recently left his position as non-executive chairman, reckons the man he nurtured as a future boss deserves credit for accepting a pay cut at all.
He said: "People have to remember that contract was signed when Rangers were in the Premier Division and had an opportunity of getting to the Champions League.
"That's where that started and I don't think it was any of his doing that Rangers have ended up in the situation they're in.
"They've adjusted to that now, everyone has made it clear what's going to happen, and Alistair has agreed to take a cut.
"It's good of him to do that because he's put his career on the line - I don't think he'd ever have imagined managing Rangers in the circumstances that they find themselves in."