Shire silenced Ibrox when they took the lead through Andrew Stirling five minutes before the break but a second half double from Andy Little and a goal for skipper Lee McCullock saw Rangers to a 3-1 win.
The victory came just 48 hours after the club learned that Rangers would not be stripped of the trophies they won between 2001 and 2011.
An independent commission - chaired by Lord Nimmo Smith - ruled that no sporting advantage was gained as a result of the non-disclosure of some payments to players relating to Employee Benefit Trusts.
"It's been a fantastic 48 hours for the club and it ended really well," said McCoist. "The first 45 minutes obviously weren't great but the victory was the most important thing. It's been a great day."
Celtic issued a statement declaring their shock at the ruling handed down by Lord Nimmo but McCoist said: "I was neither surprised nor disappointed to be honest with you.
"It went to a commission with Lord Nimmo Smith and two very prominent QCs. You would have to say that's what Lord Nimmo Smith does for a living, making decisions.
"I'd have to say he's very good at it. So I would rather take his decision than anybody else's so we are delighted."