"We have got players coming back from injury and a big and deep squad so 2016 is looking positive," Carroll told the club's website (www.whufc.com).
The Hammers were winless in eight games heading into Monday's game, with their last victory and Carroll's last goal coming in the same game -- a 2-1 win over Chelsea in October.
"It has been eight or so games since we won so we are all delighted and I am just glad we got the win in the end," the former Newcastle and Liverpool player said.
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"I have had a little niggle so it was great to be back out there."
Manager Slaven Bilic praised his side's mentality after they fell behind to a Carl Jenkinson own goal and came from behind to win for the first time this season.
"We showed a change (after half time) in character, a change in determination and a change in attitude," Bilic told reporters after the game.
"To be fair, they could have been two up at half time, but they were not, and nobody can say we did not deserve it in the end.
"It's great for the players who came back and it is good motivation because we are expecting even more players to come back."
The win moved West Ham into seventh after 19 games on the league table, a point behind sixth-placed Manchester United. West Ham play Liverpool at home on Saturday.
(Reporting by Nayan Das in Bengaluru; editing by Sudipto Ganguly)
