Ninety-six fans were crushed to death at Sheffield Wednesday's stadium as Liverpool took on Nottingham Forest in an FA Cup semi-final on April 15 1989.
In a moving tribute Dalglish, who was manager of Liverpool at the time of the disaster, speaks about the events at Hillsborough on camera for the very first time in a documentary to be broadcast on the 20th anniversary of the disaster.
He joins families who lost loved ones, survivors, and players as they discuss what happened on that fateful day in Sheffield.
Dalglish said: "The easiest thing to do is just to put the kick-off back a bit. That's no problem for anybody.
"If the police are talking to the FA and the FA have got to make that call, there wouldn't have been any resentment or disagreement with the people in the dressing room, neither Brian Clough nor ourselves certainly.
"It's something that everybody wished had never happened but I think it's also something that nobody should forget."
Dalglish added: "We made sure somebody with Liverpool connections was at every funeral and I think the families really respected that.
"The boys weren't obtrusive in any way, they sat back and let the families get on with the grieving but they were there, their presence was there, but they didn't need to have anybody coming up and telling them how grateful they were to have been there, they were there because they wanted to be there."
Hillsborough Remembered is on the History Channel on April 15 at 8pm.