Dalglish became emotional on television discussing the triumph.
And Robertson says: "For The King to be emotional means we've done something pretty well.
"He was brought up as a player and a manager here and he was used to success — winning league titles and the Champions League year-in and year-out.
"For this club to go 30 years without winning the league was something we had to change. That's why people were more emotional than usual. We had quite a few wet eyes in the small party we had (after Manchester City's loss at Chelsea confirmed the Anfield title triumph on June 25).