Allardyce completed the signing of England striker Andy Carroll from Liverpool for a club record £15m in June.
And it was widely reported that Allardyce was hoping to add at least one more forward to his squad during the transfer window.
Speaking to the London Evening Standard Allardyce confirmed he did try to bring fresh faces in.
Allardyce said: "Jermain Defoe, Loic Remy, Romelu Lukaku, Demba Ba, two players from Juventus and Austrian international Marko Arnautovic, who joined Stoke, were all on our radar at one stage or another but for varying reasons, none of them came."
One player Allardyce was pleased to capture though was England winger Stewart Downing from Liverpool.
Allardyce added: "Stewart Downing, who had become available a little earlier, is an outstanding player who will be invaluable to us.
"I emphasise that because there has been some criticism out there that, instead of signing him, we should have waited for a striker."