Scot believes his side have suffered from contentions decisions in every Premier League match this season and will discuss how to approach the issue with the club's owners
The veteran manager repeatedly and pointedly said that he would consult the club's owners about what course of action to take after his side saw decisions go against them when they went down 1-0 in controversial circumstances.
He told reporters: "We can only do what we can do ourselves, sometimes things are taken outside your jurisdiction, and if you continue to play like that – with the commitment – we'll be OK this season.
"But if we continually get battered by things that are outside our control then we're not going to have much chance.
"The first four league games have all had a contentious decisions and every one has gone against us.
"We would like to be respectful to the referees and I think we have been respectful to the referees, but more important than being respectful to referees and their campaign is having respect for my football club, our football club, Liverpool Football Club, and if I feel that they're suffering in any way, shape or form, I'll need to go the same route some other people do, and see if we can gain some benefit from that.
"I'll speak to the owners first, see what they say because the last thing I want to do is for my behaviour to impinge on the club's success in any way, shape or form."
Asked what options he could take, he repeatedly stated: "I'll speak to the owners first."
Stoke City's goal came via a contentious penalty after Jamie Carragher was deemed to have illegally brought down Jonathan Walters, who converted from the spot, in the area after both players battled in the box.
Dalglish added: "We don't have any complaints, for want of a better word, about Stoke City.
"They played very, very hard. They played well. They got their goal and they defended their goal courageously at times, maybe occasionally they got a bit of luck.
"We don't have anything but appreciation for the way that they played and the way they held on to the game and [went] on and won."
However, he added: "I just can't see how that it's a penalty kick. I just can't."
Liverpool squandered several chances in the game and Dalglish was pleased with his players' efforts.
He said: "We're very disappointed with the result. We're delighted with the effort and the commitment of the players, and on another day we could have had three or four.
"I don't think there was anything wrong. Although the passing was not as good as it has been, it was still good enough and we still did enough in the game to have scored three or four goals, unfortunately they never came.
"Credit to Stoke, they scored their goal, defended heroically and won 1-0.
"There's not much more we could have done other than that bit of luck and a bit more accuracy in front of goal."
The Reds were guilty of missing several gilt-edged opportunities to score, with Luis Suarez in particular missing a chance in injury time after Asmir Begovic had spilled the ball.
"You think it's an easy chance but it's not when you see it on television, when you see it on that big screen that was up there – which conveniently went off a few times," he added.
"The goalkeeper's got a good angle on it, it's a difficult chance to take."