Marsch was sacked as Leeds manager last week, but it seemed he could be appointed as the Southampton boss this week.
However, talks broke down between Southampton and the American and he will not be taking charge of the Saints.
Marsch was not ready to accept the short-term contract Southampton were offering until the end of the season and wanted a longer deal.
And Leeds legend Giles indicated that it was a derisory offer from Southampton and Marsch was right to walk from that.
He feels the Saints were demanding a miracle from the American for him to get an extension to his stay.
The Leeds legend stressed that Southampton must offer a deal until the end of next season if they want a new manager.
Giles said on Off the Ball: “I think the offer wasn’t very good, to be honest.
“What they were saying was if you keep us up, we will extend the contract so what they were saying was, if you don’t keep us up you are gone.
“That’s not the way to do anything, I don’t blame him for walking away from that.
“What they wanted is a miracle for him to get an extension on his contract.
“That’s not the way to do it.
“If they are serious then get a manager and appoint him now for at least 12 to 18 months.
“I think it’s outrageous to do what they have done with Marsch because he was under the impression that he was going to get a contract until at least next season.”
Southampton are said to have postponed their search for a new manager until after their game against Chelsea this weekend.
