"Two things cost us victory today, our finishing in the first half and the referee. There was a blatant foul on Hierro on the build-up to their first goal.
"I know Keith Hackett (the Premiership referees' supremo) was here today, and I hope he does something because the standard of refereeing is just not good enough."
Allardyce did however applaud Chelsea's achievement, adding: "I don't want this to detract from what Chelsea have done this season.
"They are worthy champions. But in saying that, had we had won today it would have taken us into Europe, a magnificient achievement for us, and that's why I'm so bitterly disappointed."