The Hammers broke their record transfer fee to sign Andy Carroll, while goalkeeper Adrian, full-back Razvan Rat and midfielder Danny Whitehead have all moved to Upton Park.
Allardyce is pleased with those additions and believes they will benefit his side.
"This has been one of the quietest summers I've had," he said. "We have done some good business.
"Andy Carroll has come in, we've got a new goalkeeper in Adrian from Real Betis, who seems to be settling in very well, and Razvan Rat will help strengthen the defence."
Despite having England international Carroll among their ranks, it is believed adding another striker to the squad remains a priority.
Carlton Cole was released and both Wellington and Marouane Chamakh returned to their parent clubs after loan spells last season, and with Carroll unlikely to feature in West Ham's season opener against Cardiff, Allardyce is light up front.
Former Chelsea forward Salomon Kalou have been heavily linked with a move to Upton Park and Allardyce has said it is likely only one more acquisition will be made.
"We're looking at securing one more player within the budget we've got this summer, and hopefully that will make us a little bit better than last season," he said.