The Rangers legend was quick to sing the praises of the veteran midfielder after he produced an influential showing as the Ibrox side dumped their neighbours out of the Scottish Cup and advanced to the quarter-final stage.
This included a terrific opening goal where Davis beat keeper Scott Bain with an overhead kick.
McCoist said on Premier Sports: “I thought he was out of this world today. I honestly did.
“The goal was special, but I think he just controlled everything: he was in those little pockets, picking everything up.
“It’s incredible with the season he’s had and he continues to go strong for Northern Ireland, where he’s the most capped player in Britain.
“It might have been harsh not giving man-of-the-match to Nathan Patterson because he was fantastic. But I just don’t think you could overlook Davis’ performance.”