Adam calmly slotted into the net from the penalty spot early in the game before Carroll secured the points with a low drill beyond Ben Foster.
"The big man has been unbelievable today and the finish for our second goal was terrific," he said.
"Once we got the goal it changed the complexion of the game. I thought we played well in the first half. Second half, we never kept the ball as well as we should have and it's something that we'll maybe have to get better at.
"But to come here and get three points has delighted us.
"We're disappointed with some of the results we've had this year. Last week (v Norwich) we had numerous chances and could have finished it off but that's what happens when you play in the best league in the world. If you don't score you can get punished, and we did.
"We've done that a couple of times this year but today we've started the game very well and deserved to win the game in the end."