The Hammers signed Mladen Petric as a free agent last week.
Allardyce wrote in the London Evening Standard: "I have been asked why we were at pains, before the transfer deadline, to point out that we had reached our maximum wage cap under the new rules yet still managed to find the resources to sign Petric.
"The truth is that we were near our maximum - but there was some leeway, which is why we've been able to sign him.
"In the meantime, players such as Modibo Maiga have a massive opportunity to step up to the plate.
"He hasn't scored yet and he didn't play well against Stoke but only the back four and the goalkeeper were up to scratch in that game."
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