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."