Lukaku hit the winner six minutes from time after two brilliant Leighton
Baines free-kicks hauled the Toffees back into contention as the Upton Park
showdown reached a dramatic conclusion.
Allardyce pursued Lukaku throughout the summer only to be told by Chelsea
manager Jose Mourinho he was staying at Stamford Bridge.
But Demba Ba's deadline-day decision to stay with the Blues forced a rethink
and Everton beat West Ham and West Brom to the signing of the 20-year-old, who transformed the match with his arrival at half-time.
"It was frustrating when he scored. I'd been talking to Chelsea all summer -
will he move, won't he. I was told no, no, no," Hammers boss Allardyce said.
"Then Ba decided to stay and there was a quick shift around with a few hours
to go and Everton got there before us and West Brom. That's the way the cookie crumbles."
Allardyce disagreed with the dismissal of Mark Noble for two yellow cards, the
second coming shortly after he had scored a penalty and moments before Baines fired his second equaliser.
Choosing his words with care, Allardyce indicated that he felt referee Lee
Mason had endured a poor afternoon and declared officials should be more open to criticism.
"I have to be careful about what I say - we all have to be careful because we
get pulled up on what we say to the referee. We get fined," Allardyce said.
"Do I agree with it? No, because that's the wrong sort of protection for
referees as far as I'm concerned.
"If we want to make them better than they have to be criticised like us all.
For me to say too much about how I thought the referee performed, I'd get myself into trouble."