The £35 million January signing produced arguably his best performance of the season thus far on Saturday, hitting the post and coming close with another chance in the 2-1 victory against Wolves.
And whilst the Spanish defender is hoping Carroll's first goal of the campaign comes in the Merseyside derby against Everton next weekend, Enrique believes the building partnership with Luis Suarez can benefit the pair.
"Andy was unlucky not to score. Maybe he tried too many tricks with the chance at the end but I think next time he will score," said the left back.
"Against Everton would be the perfect game for him to score.
"I think he and Luis Suarez complement each other well.
"Every day I see how good Luis is. Everyone knows if he's in form he's one of the best strikers in the world. Of course he's still young and still has a lot to learn but if he continues the same way he will be one of the best for a long time."
Attentions have immediately turned to Saturday's derby against the Toffees, with Kenny Dalglish's side traveling to Goodison Park and looking to move into the top four.
Whilst Enrique acknowledges that the game has extra spice because of the rivalry between the two clubs, claiming three points and pushing towards the Champions League positions is the most important thing for the 25-year-old.
“The derby is a massive game but the most important thing is the three points. If we want to get one of those Champions League positions then we need to win these type of games," he continued.
“If we can get another three points before the international break we will have done well.
“We should have scored more goals against Wolves but the main thing is we made a lot of chances.”
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