The 2-0 loss means the Hammers finish the season in 12th place after being in the Champions League spots at Christmas.
After picking up 31 points from their first 17 matches of the season to be in fourth heading into the Boxing Day fixtures, the Hammers have won just three of their remaining 20 matches to pick up just 16 points.
Only Newcastle, Queens Park Rangers and Burnley have picked up fewer points in that period.
After four years under Allardyce, West Ham will want to appoint a manager who can play a more attractive style of football and lead the club forward with the move to the Olympic Stadium just around the corner.
Additional reporting from PA
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