Dalglish described as “totally wrong” requests from former FA chief executive Graham Kelly for silent tributes to the late prime minister at Barclays Premier League and FC Cup games this weekend.
The Scotland star was manager of Liverpool FC on 15 April, 1989, when a crush in the stadium led to the death of 96 people.
Kelly, meanwhile, was head of the FA at the time of the tragedy, which occurred the year before Thatcher resigned as prime minister.
Last year David Cameron apologised after an independent inquiry found that police had deliberately altered more than 160 witness statements in an attempt to blame Liverpool fans for the fatal crush.
The panel reported that crowd safety was “compromised at every level” and that 41 of the 96 who died could have survived.
In his column for the Mirror newspaper yesterday, Dalglish said: “Let’s have nobody trying to jump on a bandwagon and use [the Hillsborough anniversary[ for anything else.”
He added: “If the FA, in their great wisdom, wanted to plan a tribute to Mrs Thatcher, let them do it another weekend. Not this one.
“And while Mr Kelly is talking about ‘appropriate levels of respect’ for the former prime minister, maybe he should apply that to Hillsborough too.”