The Upton Park club, who finished 13th in the Premier League last year, have made four summer signings so far to strengthen the squad - Argentine forward Mauro Zarate, Senegal midfielder Cheikhou Kouyate, left-back Aaron Cresswell and promising midfielder Diego Poyet.
Sky sources understand Ecuador striker Enner Valencia is lined up as the next arrival and could arrive in the next 72 hours.
"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.
"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."
Former West Ham striker Teddy Sheringham has also re-joined his old club as part of the coaching staff.
Allardyce has every confidence in the appointment, and sees the 48-year-old as an integral part of his new goal-scoring strategy.
"Teddy is someone I have known for many, many years," Allardyce said.
"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."
After a busy summer transfer period, Allardyce and joint-chairmen David Sullivan and David Gold are not yet finished in their recruitment drive and Sullivan announced on Saturday that a fifth signing - expected to be Valencia - was in the offing.
West Ham kick off their 2014/15 campaign at home to London rivals Tottenham Hotspur on August 16.