A lack of goals undermined Allardyce's side last term as they finished 13th in the Premier League.
The London club could only find the net on 40 occasions, with fans expressing their discontent at a lack of on-field entertainment on several occasions during the campaign.
West Ham's board subsequently made Allardyce aware that greater attacking flair is expected in the 2014-15 season.
And, following the appointment of Teddy Sheringham to the club's coaching staff, the experienced manager is eager to see an improvement from his club's strikers.
"It wasn't about the fact that we didn't create chances last year; it was the fact that we didn't convert enough," Allardyce told Sky Sports News prior to Saturday's 2-2 pre-season friendly draw at Stevenage.
"That's what it came down to last year, really - had the goal tally been six or eight more, we would actually have finished in the top 10.
"The emphasis is going to be on opening the opportunity again and making sure we convert more of those chances."
On the arrival of former England striker Sheringham, Allardyce added: "Teddy is someone I have known for many, many years.
"He's had a long spell out of football since he retired, after a fantastic career that lasted well into his forties. Now he's hungry and ready to give something back.
"We hope that he can bring in a new phase, a couple of different ideas, and specifically work with the front men to score a few more goals."
West Ham co-chairman David Sullivan announced on Saturday that a fifth close-season signing was close to completion, to follow the arrivals of Mauro Zarate, Cheikhou Kouyate, Aaron Cresswell and Diego Poyet.
Allardyce said: "We're very close, but nothing is ever certain in this game with new signings until they have actually signed on the dotted line."
