West Ham had been expected to tie up a deal for Diarra in the coming days after the French midfielder was released by Russian side Lokomotiv Moscow in August.
Diarra, 29, had been training with West Ham in the view of earning a contract but Allardyce told reporters following Wednesday's goalless draw against Southampton that the former Real Madrid man would not be arriving at Upton Park.
"We have waited and we have negotiated for weeks to get the right deal and now we've got it, we find we can't get the right paperwork and the right clearance, so we have wasted his time and our time," said Allardyce.
"On the basis of the situation we're in right now he would have been a very crucial player for us between now and the end of the season."
Diarra, who earned 28 caps for France between 2007 and 2010, claimed FA Cup titles with Chelsea and Portsmouth, while he tasted success during his three-year stint at Real Madrid, winning La Liga, Copa del Rey and the Supercopa de Espana.
