The England international has failed to make an appearance for the club this season, having signed from Liverpool in June, but is back in training following a foot injury.
West Ham co-owner David Sullivan this week admitted that if the club knew Carroll was going to spend so much time out injured, they "would not have signed him".
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Allardyce understands his employer's view, but insists the £15 million deal to bring him from Liverpool in the summer made perfect sense at the time.
"He [Sullivan] said, 'Only at the end of the season will we be able to judge whether Andy Carroll is a good investment'," the Hammers boss told reporters.
"[Given] the size of that investment I can understand why he's said that.
"It's not [Carroll's] fault he's injured, he's the difference between us winning more games and us not.
"If you look at our win ratio with Andy Carroll [compared] to without him, it was pretty obvious [in the close season] we should sign him.
"It's like Manchester City not having [Sergio] Aguero or [Alvaro] Negredo."
Allardyce believes a lack of belief, as well as absentees through injury and suspension, have caused West Ham's form to dip in recent weeks.
"You wouldn't say [the performance was] 'one of those things'. I would look at the nervous tension that I have to relieve around the place at the minute," he continued.
"This game was no bigger than the Fulham game two weeks ago. Both teams needed a win and we played a fantastic game and won comfortably 3-0.
"Today we didn't see that. I've picked up a lot more injuries and suspensions since then, so my squad has got thinner.”