The Uruguayan was a constant threat to United's defence at Anfield last term and despite only Dirk Kuyt's name being on the scoresheet for the 3-1 victory, Suarez gained all the plaudits following a number of impressive pieces of individual skill during the match.
The 24-year-old has continued to influence Dalglish's side during the new campaign and the Liverpool manager believes his star striker has the potential to damage United once again.
"I think the problem opponents have with Luis is that they don’t know what is coming next, but he does and that’s helpful. We just hope he continues to surprise us - but pleasantly!” Dalglish told reporters.
“Whether his performance last time against United will give them a psychological scar, that is up to them. I don’t know how they think but I’m sure they will know what he did to them last season.
“They know what he is capable of and that is their problem. He does something different every time you see him. Everyone can see what he has done on the pitch but he is a fantastic personality in and around the place.
“That run against United, I don’t know how he did it – honestly, I’ve no idea.
“But it’s not the first time he’s done that. Maybe it was in terms of how many he went past, but each of the individual things he used to get past people he had done before.
“He just collated them in the one run past three or four. But he has got other things to his bow apart from that. He did fantastically well for that first goal and obviously the game has got happy memories for Dirk Kuyt as well.”
Dalglish also praised Manchester United and Sir Alex Ferguson for their success over the years, insisting money is not the sole contributor to the club's dominance within English football.
“There is no point burying your head in the sand, they are a fantastic football club that has been hugely successful and there is no way anyone can or should argue with that,” said Dalglish.
“Fergie has made a massive contribution to their success. Sure, financial factors play a huge role at all clubs, but finance does not guarantee success, it helps.
“Everyone who has been successful has had good financial support, but we want to move forward and upwards and we will see where it takes us.
"Where that is, at this stage, I don’t know.”