Carroll nodded Craig Bellamy’s cross past Everton goalkeeper Tim Howard in the 87th minute after Luis Suárez had earlier cancelled out Nikica Jelavić’s first-half strike.
Henderson, who moved to Liverpool from Sunderland last summer, highlighted Carroll’s important role at the club despite the England striker’s lack of goals this season.
“I’m over the moon for Andy,” Henderson told Liverpool’s website.
“He works hard every day in training and I think he works really hard for the team. As you saw against Everton and last week, he scored two winning goals in two massive games.
“So you can see that the quality is there and he’s got belief in his own ability. It’s brilliant to see. I think we deserved it. First half it was a little bit even but second half we came out and started really well.
“It was a massive game for us but we came through in the end. We were a little bit disappointed with the first half performance but second half we came out of the blocks really well, we had a few chances to win it and we put them away.”
Henderson won his first trophy with Liverpool when the Reds beat Cardiff City 3-2 on penalties in the Carling Cup final in February, and the 21-year-old is targeting more silverware when Kenny Dalglish’s side face Chelsea in the FA Cup final on 5 May.
“We won the Carling Cup this season and now we’ve got another final,” added Henderson.
“I think we’ve still got to concentrate on the league and finish as high as we can.
“It was a brilliant atmosphere. I think everyone expected that and it was brilliant to hear You’ll Never Walk Alone again at the end of the game.”
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