Dalglish maintains Suarez has not been treated fairly and claims the full facts of the affair have not been made public.
The club have chosen not to appeal against the Uruguay international’s eight-match suspension for racially abusing Manchester United defender Patrice Evra during the 1-1 draw in October.
That decision came after they analysed the 115-page document released by the independent commission on New Year’s Eve.
It meant the forward began his ban immediately, missing Tuesday’s 3-0 defeat at Manchester City.
But despite the commission’s report damning Suarez for providing “unreliable” and “inconsistent” evidence at the hearing, Dalglish claims the report does not tell the full story.
Both the club and Suarez issued statements on Tuesday evening in which they refused to accept responsibility and criticised the whole process.
However, Dalglish refused to say exactly what the report failed to contain, citing further retribution from the Football Association for his reticence.
“We have made a statement and I think it is there for everyone to read,” he said.
“Luis has made a brilliant statement and we stand by him.
“There are a lot of things we’d like to say and a lot of things we could say but we don’t want to get ourselves into trouble.
“We know what has gone on; we know what is not in the report and that is important for us.
“But without me getting myself in trouble, that is me finished.
“It is unfortunate that you don’t actually know the whole content of what went on at the hearing.
“I am not prepared and I cannot say. I cannot go any further.”
When asked whether the statements issued would only ensure the row would rumble on, the Scot added: “I don’t think we are digging a bigger hole – it is unfortunate we cannot be more forthcoming.”
Dalglish also defended the much-criticised decision by the players and himself to wear T-shirts in support of Suarez at the Wigan match before Christmas.
“If one of your guys was in trouble would you help and support him if you knew it was the truth and you knew it was right,” he said.
“If they want to show their support for their team-mate, what is wrong with that?
“I think it is a fabulous statement to make visually of your support for a guy
who is endeared in the dressing room.”