"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," he said following his team's 0-0 draw at Southampton on Wednesday.
"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 has been without a club since leaving Lokomotiv Moscow in August and has not played in almost nine months.
The former Real Madrid player had been training with West Ham and the 29-year-old was keen to revive his career back in England where he previously played for Arsenal, Chelsea and Portsmouth.
"As soon as we get him fit he will be a very good addition to our squad," Allardyce told a news conference on Tuesday.
West Ham have been hit by a spate of injuries over the last few weeks and have slipped from fourth spot in late December to eighth in the table with just one win in their last eight league games.
Of fresh concern to the Hammers, who face West Bromwich Albion in the FA Cup fifth round on Saturday, is another injury suffered by striker Andy Carroll who aggravated a knee injury against Southampton but had to remain on the pitch because West Ham had used up all their substitutes.
"I just hope staying on hasn't made the injury any worse," said Allardyce whose side finished the match with 10 men after goalkeeper Adrian was sent off for handling outside his area.
(Reporting by Mike Collett; Editing by Amlan Chakraborty)
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