Warburton's side brushed aside last night's opposition as two goals from Martyn Waghorn sent Rangers into a comfortable 2-0 half-time lead, before summer signing Niko Kranjcar put the game to bed on 53 minutes.
McKay was a threat to Stranraer throughout and won the penalty which led to Rangers' opener after five minutes, and the 53-year-old manager acknowledged his midfielder's performance on the night.
"Barrie's been outstanding. He's come in and he was a week behind the boys - we saw that at Charleston maybe - but he's caught up," Warburton said to Rangers' YouTube channel.
"He's a good athlete, Barrie, technically outstanding. But he's impacting games. He is learning all the time how best to use his ability.
The Blues had a rigorous examination of the strength of their squad due to four League Cup outings in the space of nine days, but Rangers passed that test with flying colours by winning all four, scoring 10 times and conceding none.
Their excellent form certainly sends out a warning to their Premiership rivals. It seems as if Rangers - who have signed no fewer than nine new players this summer - will be a threat this season and the fans, starved of top-flight football for four years, must be relishing the new campaign.
They kick off their Premiership campaign by hosting Hamilton at Ibrox on August 6, after facing Premier League side Burnley in one last game before then.