Building on a midweek battering of Falkirk, the Inverness side struck down the Dumfries men with goals from Iain Vigurs, Joe Chalmers and Aaron Doran.
While a late reply from Owen Bell lofted Queens back above the hosts on goal difference, Robertson said: “We asked the players to finish off this sequence of five games in 15 days and leave nothing out there.
“That’s exactly what they did.”
A highly-entertaining first half ignited after only three minutes. Queens’ keeper Jack Leighfield tipped a Gary Warren header onto the bar but, from Liam Polworth’s corner, Brad Mckay nodded across goal and Iain Vigurs slammed a header into the top left-hand corner.
Stephen Dobbie missed a sitter for the visitors from five yards after 21 minutes and a free-flowing Inverness took full advantage of that let-off eight minutes later. As another Polworth corner was knocked clear, Joe Chalmers struck a 25-yard left foot shot low through a crowded penalty area past the unsighted Leighfield.
Just before the hour, Polworth’s cutback set up Doran for the third, driven through the flailing grasp of Leighfield from 15 yards.
Substitute Owen Bell headed home a consolation from Scott Mercer’s cross with four minutes left.