Striker Mackail-Smith signed a four-year contract with Gus Poyet's side despite Peterborough receiving bids from the Hammers and Leicester.
The Scotland international was also linked with Premier League newcomers QPR and Norwich, but instead opted to join last season's League One champions.
Upton Park boss Allardyce now has to look elsewhere to bolster his strikeforce ahead of the Championship season after losing out to the Seagulls.
He said: "We did table a bid for him and strangely enough I think he chose Brighton so I'm not quite sure what went on there
"No disrespect to Brighton, but it seems more of a financial move than a football move."