Constellation chief executive Richard Sands said the firm did not "believe the the economics justify an offer. Simply put, careful consideration and evaluation of the details following due diligence did not identify sufficient value for submitting an offer."
Constellation, the world's biggest wine company, had led a consortium, including US spirits firm Brown-Forman as well as private financiers Lion Capital and Blackstone, in a preliminary approach for Allied.
But, analysts cast doubts over the group's ability to find the necessary funds for an offer that could beat the £7.4bn (€10.3bn), 80 per cent cash, deal already on the table from Pernod Ricard.
The departure of the consortium now leaves Pernod as the only bidder with Allied set to hold an extraordinary general meeting in Paris on 30 June for shareholders to vote on the offer.
In April, Allied agreed to pay Pernod £37 million if it was beaten by a competing offer within the next six months.
Pernod will become the world's largest wine and spirits group if successful, grabbing core spirits brands such as Beefeater gin, Malibu and Stolichnaya vodka as well as premium wines including Montana and Campo Viejo.
The firm plans to sell a range of Allied's brands, including Canada Club and Courvoisier, to US firm Fortune Brands for £2.8 million (€4.1 million) cash to avoid infringing competition laws.
Any company acquiring Allied may also look forward to cost savings that greater consolidation could bring. Philip Bowman, chief executive of Allied Domecq, said consolidation was increasingly necessary in spirits due to tough economic and competitive conditions.
Allied recently announced a seven per cent rise in net profits to £285 million, though overall sales were flat at around £1.7 billion. Sales of spirits and wine crept up one per cent to £1.236 billion.
Allied's shares were valued at 675.5p each at the time of publication.