Carroll was introduced as a late substitute in a closely contested third-round tie at Upton Park, and he provided the pass for Nikica Jelavic to break the deadlock with a superb 84th-minute goal.
Carroll scored against his former club Liverpool in West Ham’s previous outing, and he received a glowing report from his manager after helping the Hammers into the fourth round of the cup.
Bilic said: "Andy Carroll was important in being introduced because he is in good form and he must now stay fit, because he looks capable of doing many different things on the pitch.
"He can do hold up play without training, chest it, play with it at his feet.
"He needs fitness and now he looks like he has that."
The victory over Wolves left Bilic confident of his side's chances in the FA Cup – a competition he previously said he would rather win than qualify for the Champions League.
Enner Valencia and Cheikhou Kouyate were both rested against Wolves, and Bilic reflected on the strength of his squad after the win.
"The cup is there for us," he said. "We're not in Liverpool's situation with two cups and Europe. We have a big enough squad and it is good that we put out a team with different faces.
"It wasn't a big risk either because most of the side have played in the last month, and not one of them was out for a long time.
"The FA Cup is often very tough. Even when you play teams in lower leagues they can be strong, so I must say well done to the lads."