Lukaku struck 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 climax.
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 converted 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.