Beardsley is now on the coaching staff at Newcastle United.
"I watched him closely that day and he ran the game against us," the Englishman told the Liverpool Echo.
"He has such a great understanding of the game. Good players like that know when to get rid of the ball. On the odd occasion he gets caught, but not often.
"He's very clever - he's always aware of where his teammates are and how they want the ball. Some of his passing takes your breath away and he has a great attitude as well.
"It was a smart signing by Brendan. I don't think anyone saw it coming and he was a real bargain.
"I love Coutinho; he is outstanding and has unbelievable ability. He's better than I ever was and I really mean that. He's miles better than me.
"If he stays here for a long time he's got a chance of being as big as Kenny - that kind of stature. I look at his ability and I think he could be the new Kenny Dalglish. He is a very special player."
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