A goal in each half from Joe Cole and Kevin Nolan sealed a win for West Ham in their opening Premier League fixture against Cardiff City at Upton Park
A goal in each half from Joe Cole and Kevin Nolan sealed three points for Allardyce's men, who were criticised last season for a direct-style approach.
Allardyce, however, dismissed suggestions that his side are focussed too heavily on their defence and believes his players could have scored more against Malky Mackay's men.
"We've perhaps not taken as many chances as we would have liked but that doesn't matter. It's a 2-0 victory, it's a clean sheet and it's two very good goals," he said.
"It's that old adage about us playing one up front, which is a load of bull.
"Sometimes we play one up front when we play Manchester United, most teams do, but when we play here we play with a front three.
"That was abundant today, so let's hope that continues at Newcastle next week and we pick more points up."
Cole was singled out for special praise by his manager after his 13th-minute goal put the home side ahead against the Premier League newcomers.
And another player who impressed Allardyce was recent signing Stewart Downing, who replaced Matt Jarvis after 71 minutes.
Speaking about Cole, Allardyce said: "Timing his runs and knowing where to run is what Joe is all about."
While on his latest acquisition, Downing, the West Ham boss added: "It was pretty exciting what he contributed and he's glad to be here, which is the most important thing."
Allardyce also confirmed that Downing began his first game at West Ham on the bench because of a lack of match fitness, while Andy Carroll is still struggling with a heel injury.