The Reds have lost six of their last seven Barclays Premier League matches.
Barnes, one of the star signings of Dalglish's first stint in charge, told BBC Sport: "We're in the results business and Kenny is no different to anyone else.
"If Sir Alex Ferguson goes through a run of losing games, he's going to be in trouble. No matter who you are, it's a results-driven business.
"No-one is immune. There are people talking about it - we have seen it, we have heard it.
"It does happen, but you also have to be realistic in terms of the effect it will have on what you are trying to achieve.
"And the people in the know - how much are they going to support you? Kenny is well supported, so he won't take any notice of that."