Millman struggled to deal with the Pospisil’s power game in the second set and while he gamely hung in the set, he was unable to hold serve at 5-4 down and the Canadian forced an error to seal victory.
Millman has been a spectator for the first two ties of the tournament but it was announced just an hour before the start of match he would replace Kyrgios.
The world No.30 had been in superb touch in the opening two singles rubbers against Colombia and Belgium, hurling down 38 aces in just four sets and looking fully focused in both matches.
Alex de Minaur must now beat fellow young gun Denis Shapovalov to keep his country in the tournament in a mouth-watering clash between the two outstanding 20-year-olds.
The match is a repeat of the 2016 junior Wimbledon final which world No.15 Shapovalov won in three sets at the All England.
Felix Auger-Aliassime has failed to recover from an ankle injury so the undermanned Canadians must rely on Pospisil and Shapovalov in the doubles against John Peers and Jordan Thompson.
Peers has been passed fit to play after pulling up with an elbow issue in Tuesday’s doubles match against Belgium.