The Bolton manager promised them the first dozen bottles at their belated Christmas party - possibly the first two dozen. If his side's performance had not quite been premier cru, it was certainly of a far better vintage than that which has seen them stand accused of being downright unpalatable of late.
There were two obvious reasons for the return of the missing sparkle and fluency. For one thing, the pitch, so ruined by playing on it when it was virtually underwater against Zenit St Petersburg in the Uefa Cup in November, has been replaced by a new one, which ran smooth and true under the late winter sun.
For another, Bolton had back in their side the one player certain to insist that they used it in the way that nature intended.
There is a theory, to which not all Bolton supporters subscribe, that Ivan Campo should always be in the starting line-up, because he forces those around him to play football.
Campo was making only his third Premiership start of the season and he made that sort of difference as he sprayed long passes out to the wings and shorter ones to the central midfielders ahead of him."Once he blew the cobwebs away, he started to find the space for his probing and his long passing was outstanding," Allardyce said.
One of those to benefit from Campo's approach was Kevin Davies. He was asked, in the absence of El Hadji Diouf at the African Nations' Cup, to play wide on the right and he gave City's young left-back, Stephen Jordan, a gruelling afternoon, including turning and sweeping past him to set up Bolton's first goal.
His redeployment created the opportunity for Jared Borgetti to play as the main striker and to take the chance that Davies provided for the Mexican's first Premiership goal.
Bolton's second came from Kevin Nolan, who gave a typically vigorous midfield performance and could have had a hat-trick.
If Bolton's absentees in Egypt - Diouf is one of four missing - remain a recurring theme for Allardyce, then Stuart Pearce, another touted for the England job if Sven Goran Eriksson succeeds in self-destructing, has his own "Riddle of the Sands" to solve.
How can a team that played with such vigour and panache against Manchester United the previous week lapse into such limp anonymity at the Reebok?
They failed to direct a single effort on target over the 90 minutes, giving Bolton their 12th clean sheet of the season and further cause for satisfaction on a very gratifying afternoon for Allardyce.
Goals: Borgetti (37) 1-0; Nolan (41) 2-0.
Bolton Wanderers (4-3-3): Jaaskelainen; O'Brien, Ben Haim, N'Gotty, Gardner; Nolan, Campo, Fadiga (Vaz Te, 22, Hunt, 89); Davies, Borgetti (Jansen, 79), Stelios. Substitutes not used: Walker (gk), Fojut.
Manchester City (4-4-2): James; Jihai, Dunne, Distin, Jordan; Sinclair, Barton, Ireland, Riera (Sibierski, 67); Vassell (Croft, 76), Cole (Fowler, 67). Substitutes not used: Musampa, Onouha.
Referee: R Styles (Hampshire).
Booked: Bolton Davies, Ben Haim; Manchester City Jihai, Sinclair.
Man of the match: Campo.