The Hammers suffered their second successive loss in the league, as they went down 4-3 to the Cherries at the Boleyn Ground.
In what turned out to be a hugely entertaining game of football, West Ham came from 2-0 down to make it 2-2, but eventually they had to end the match without getting anything from it.
Midfielder Poyet, who joined Championship outfit Milton Keynes Dons on a season-long loan deal from West Ham last week, was disappointed to see his parent club suffer defeat to Bournemouth.
Gutted to see the WH boys lost today— Diego Poyet (@diegopoyet7) August 22, 2015
Over the course of the 90 minutes against Bournemouth, West Ham had 46% of the possession, took nine shots of which four were on target and earned five corners.
The Hammers also ended the game with 10 men due to the sending-off of Arsenal-owned defender Carl Jenkinson.