The England international striker, who had been in fine form for the Hammers in recent months, suffered torn ligaments in his left knee during the Hammers 0-0 draw with Southampton nearly a fortnight ago.
The 26-year-old underwent surgery on Tuesday, and his latest setback is set to rule him out for the rest of the campaign.
“Everyone is very disappointed and he's very disappointed himself,” Allardyce told WHUFC.com.
“These things happen in football, unfortunately for Andy it is happening too often. He's managed to overcome the last injury and came back and did well. I think he was getting back to his best and then a different injury happened.
“We can only hope that sooner rather than later he can overcome these problems for good. He was scoring goals and playing well, it was difficult making choices between him, Diafra Sakho, Carlton Cole and Enner Valencia because they were all at the top of their game.”
Despite the loss of the big forward, Allardyce is still able to call upon another Three Lions man in Stewart Downing for Sunday’s Premier League clash with Tottenham Hotspur.
And with a European spot well within their sights, Big Sam says his men need to recover their winning mentality against their London rivals.
"We need to rekindle our winning mentality, we've been playing very well recently but haven't been collecting enough wins. We have to maintain that level to qualify for Europe and certainly beating the big boys will be difficult but not impossible.”
West Ham travel to Spurs for a midday kick off on Sunday.