The Scottish captain was in attendance for a parade to celebrate Liverpool's two FA Cup and League Cup successes this season and was spotted with a beer in his hand during the open-top bus ride.
The images have led to Robertson coming in for criticism from some Scotland fans ahead of Wednesday's play-off but McCoist and Parlour showed their support for the 28-year-old, insisting he will be ready to represent his country.
"Is he seriously getting a bit of stick for that? Why? He can't be, no way," said McCoist on talkSPORT Breakfast. "He's been unbelievable, he's been fantastic for club and country"
Parlour also weighed in, adding: "It's ridiculous, he's got to be the fittest guy I've seen in the Premier League.
"They will always have something to moan about, that's how it is unfortunately.
"I'm sure he'll be ready to go tomorrow night. It's going to be a big, big game. He knows what's at stake everybody in that Scotland team knows what's at stake."
Liverpool were narrowly beaten 1-0 by Real Madrid in Saturday's Champions League final with the parade already planned for Sunday regardless of the outcome in Paris.
Following the festivities, Robertson took to social media to thank Liverpool fans for the incredible turn out but quickly shifted his attention to the task of helping steer his country to the World Cup in Qatar.
"Can't tell you how much that means to everyone that, best fans in the world. Now Scotland Time," he wrote, using an image of his nation's flag.
A win for Scotland over Ukraine at Hampden on Wednesday would set up a straight shootout against Wales in Cardiff on Sunday with the winner heading to the Gulf State for November's World Cup.
Scotland's last appearance at a World Cup came in 1998 in France, when they were knocked out of a group consisting of Morocco, Norway and eventual losing finalists Brazil.