The Hammers have failed to score in the Barclays Premier League since their 2-0 opening day win over Cardiff whilst club-record signing Andy Carroll remains sidelined with his heel problem.
Belgium international Lukaku was brought in by Everton boss Roberto Martinez on transfer deadline day after impressing on loan at West Brom last year.
And, ahead of their meeting at the weekend, Allardyce admitted a deal for Lukaku escaped from his clutches following a summer-long pursuit of the 20-year-old.
"I chased him all summer to be honest," he said.
"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."
With Carroll still likely to be out for some time and yet to feature since completing a permanent transfer from Liverpool, West Ham have struggled to find the back of the net.
Joe Cole and Kevin Nolan struck in the victory over Cardiff but since then the Hammers have drawn a blank in the league, drawing 0-0 at Newcastle and Southampton and suffering a 1-0 home defeat at the hands of Stoke, leaving Allardyce with a growing worry.
"We are concerned about it - there is no doubt about that," he conceded.
"It's not the fact that we are not creating chances - our quality of finishing needs to improve. Our defensive side is very good."