'It was a great day for us'
West Brom clawed one goal back in reply through a late penalty from Graham Dorrans, while Youssuf Mulumbu headed down the tunnel for an early bath after being sent off deep into stoppage time.
After sealing a convincing 3-1 win for the Hammers, Allardyce hailed Carroll's performance as his best in claret and blue.
"When you look at the overall performance and the quality of the goals, it was a great day for us," said Allardyce.
"We were glad to get out there after two weeks so they could show what they can really do again. Last time we played here it was a fantastic game but we ended up losing in the last minute.
"This time we played a fantastic game and scored three fantastic goals and got a thoroughly deserved win.
"There were three very different quality goals. The first showing Andy Carroll's heading ability, Gary O'Neil with a delicate chip and of course the outstanding volley from Andy shows it's not just about his aerial dominance, it's about the overall ability that Andy has.
"I don't think you'll see a better volley technique than that one this season. Over the shoulder, right foot volley - which is his weaker foot - right into the bottom corner.
"Andy put two goals on the end of a good performance. I think his good performances have been with us before and the fans always appreciate his ability here but he today he's shown them what he is all about.
"He's shown them his ability outside of the box and the ability he's got in the box, along with his goalscoring ability. I hope this is kicking him on to being a regular goal scorer for us in the next eight games or so and upping his total as much as he can until the end of the season.
"Andy is in a good frame of mind now and finally after a long wait he has improved his match fitness and that's why I think you're seeing the performances and goals that you're seeing.
"Finally he's there and he is enjoying himself and that is more important than anything else.
"It's a great result for us and a great performance which of course takes us ever closer to that safety margin. Now we're looking forward to playing Liverpool away next week."
But there was more heartache for defender George McCartney, who was returning from a long-term absence only to suffer a recurrence of his knee injury.
Allardyce added: "I think the only downside today was George McCartney's injury, which was a big blow to George and to us. He's only just come back and he's come off with the same thing he did last time which is his medial ligaments in his knee, it's sad.
"I would think that George will be out for the rest of the season. It's a recurrence of the same injury which is a very big disappointment for us all.
"It was important that we were 3-0 up when he had to come off because we had used all of our substitutions. What a blow it would have been if it had been any different to that.
"George has waited so long to get back and he was so eager to get on. We thought, 'let's give him a little run out now,' and save the legs of the lads who had done so well, but sadly George went down with the same injury."