Lukaku joined Everton on transfer deadline day on a season-long loan from Chelsea.
Lukaku impressed during a spell on loan at West Brom last year.
“I chased him all summer to be honest,” said Allardyce.
“But when it became the final day of the deadline we missed out and Everton managed to secure his position.
“We were more or less told he was going back to West Brom. We tried, but didn’t manage to clinch it.”
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.