The £35million forward has failed to find his best form since his arrival from Newcastle in January.
Carroll has scored three goals in 19 appearances this season and just five in 28 in a Reds shirt.
He made his first start in four matches in Boxing Day's 1-1 draw with Blackburn during which he would have scored had it not been for two good saves by Mark Bunn.
Dalglish has always backed the striker, who could face his former club on Friday, and continues to do so.
"I don't think self-belief is a problem for Andy Carroll, I don't see why it should be," said the Scot.
"There's nothing to say he's short of belief and there is no evidence he should be.
"One game he played (started) in we went down to nine men (the defeat at Tottenham) and another (the loss at Fulham) we had another sent off.
"I think yourselves (the media) have a bigger problem with Andy than anyone else.
"This week is understandable because it is against Newcastle but I don't understand the rest of the stuff."
Dalglish also said the club were still awaiting the arrival of the written verdict from Luis Suarez's disciplinary commission which banned the striker for eight-matches for using offensive words, including a reference to skin colour, towards Manchester United's Patrice Evra.
"We'll tell you when they arrive - I think they'll come on the (FA) website first," said the Reds boss, who added they had not received any news on a date for Suarez's misconduct hearing for allegedly making an offensive gesture to Fulham fans earlier this month.