The 58-year-old manager believes that because Abramovich is pumping money into the club he should be allowed to do as he pleases.
The decision to remove Di Matteo and replace him with Rafael Benitez has been an unpopular one at Stamford Bridge leading the visiting Chelsea fans at Upton Park on Saturday to chant, "Roman Abramovich, is this what you want?" As the Hammers went 3-1 up against the European champion.
"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."
Chelsea is expecting Frank Lampard and John Terry to return to training this week following injuries and Allardyce believes their absence has hit the Blues hard, but that they still should have the quality to get results without them.
"I think they're missing John Terry. I think they're missing leadership,” he added, before saying. "Look at the amount of money they've spent on the players and you can see the quality they've got.”
After taking the lead in the first half, Chelsea squandered opportunities to close the game out in the second with Fernando Torres in particular missing a couple of golden chances. West Ham were able to control the game thanks to the introduction of Mohamed Diame and Allardyce felt Chelsea were below par.
"In the second half, they didn't quite show as much resilience as they needed to, to overcome what we were doing. They couldn't change the way they played to cope with us. We changed the way we played to cope with them and expose them. They couldn't do that against us in the second half."