Carroll joined the Reds for a club-record transfer fee from Newcastle in the January transfer window, but has failed to make the expected impact at Anfield.
“For us in Newcastle Andy was brilliant and I am sure he will be brilliant for Liverpool too,” said Enrique.
“He is a very good player. When a club like Liverpool pays £35million for Andy, I know it is not lucky. It is because they think he is a good player. I am sure he is going to do a lot of things for us.
“I watched him play last season and I knew he wasn’t fit here. I don’t care if the player is Messi or Cristiano Ronaldo, if a player is not fit, he is not fit.
“Now he’s okay, is playing very well in his position and is going to be an important player this season.”