The Hammers have completed deals for goalkeeper Adrian, full-back Razvan Rat, young midfielder Danny Whitehead and also broke their record transfer fee to sign Andy Carroll on a permanent deal from Liverpool.
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 told talkSPORT. "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 the club's priorities.
With Carlton Cole being released and both Wellington and Marouane Chamakh returning to their parent clubs after loan spells last season, Allardyce will be light up front going in to West Ham's opening league fixture at home to Cardiff, with Carroll unlikely to feature due to a heel injury.
The likes of Lille 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 added.