Reds striker Luis Suarez has begun serving an eight-match ban for racially abusing Manchester United defender Patrice Evra and the club have apologised to Oldham defender Tom Adeyemi after he was apparently the subject of racist abuse from a supporter at Anfield during an FA Cup tie last Friday.
The club were criticised in some quarters for their staunch defence of Suarez, with Liverpool players wearing t-shirts in support of the Uruguayan as they warmed up to play Wigan before Christmas, just after the eight-match punishment had been handed down.
But Dalglish stood by the decision to support Suarez and insisted he would never have returned to Liverpool if he thought the club was in any way discriminatory.
He told the club's official website www.liverpoolfc.tv: "Over the past few weeks there has been a perception that the football club isn't doing what it should be doing, but I don't think the football club would ever go down that road. We will always support the official campaigns related to racism.
"Obviously there was a big issue with Luis. The players showed support for Luis which was fantastic, but then some people interpreted that wrongly as the players saying they're not interested in the fight against racism.
"That is totally and utterly rubbish. If we can help to eradicate racism or discrimination from any part of the society, with the help of anybody at Liverpool Football Club, then that help will be forthcoming.
"We don't want racism anywhere near football and certainly not anywhere near this football club."
Liverpool opted earlier this month not to appeal against the length of Suarez's punishment having received the full written judgement from the independent commission appointed by the Football Association to hear the case.
A 20-year-old man arrested on suspicion of racially abusing Adeyemi was released on bail on Sunday.
The man, from Aintree, was arrested on Saturday by Merseyside Police, who are investigating the incident.
Dalglish said: "All we can say - it's a police matter - is if Tom, the police want any help in any way, shape or form then we'll give it to them. For me, the most important thing is that as a football club we all stick together. We all have a responsibility to act responsibly."
The Scot does not believe Liverpool would have the worldwide following they enjoy if they were perceived as being racists.
He said: "Our football club is based on being a football club serving the community, and whoever is in the community we will treat as an equal.
"It never has been a club that's discriminated and never will be one that discriminates against anyone else.
"For us, the football club is more important than any one individual, whether that person be a supporter, a player or the owner. It's not about the individual, it's about the football club and we should be very proud of this football club."