The Russian billionaire came under scrutiny last month for his decision to sack manager Roberto Di Matteo despite leading the club to the Champions League/FA Cup double whilst caretaker boss last season.
Plenty of critics have defended Di Matteo, saying he was extremely unlucky to have got the axe, but Hammers manager Allardyce feels the amount of money Abramovich has pumped into the Southwest London club allows him to make any decision he likes.
"Roman is the owner of Chelsea Football Club and he's entitled to do whatever he wants because of the amount of money he puts behind the team," Allardyce told reporters.
"He's been a great advocate for why the Premier League has become such a great brand around the world of football, by the money he's put in.
"What he wants, you have to deal with if you're the manager. And you have to deliver."