The Uruguayan marked his Anfield debut with the victory-sealing goal with about 10 minutes remaining after Raul Meireles had put the home side ahead just after half-time.
Dalglish was so happy for the former Ajax Amsterdam man who received rapturous applause from the Kop.
"I am delighted for him - and for Raul for getting the first goal," said Dalglish.
"He had not even had the opportunity to train with us because of administrative stuff which had to be sorted out.
"When he starts training with the lads I think we might see an improvement.
"He has a big smile on his face every day. He's a happy guy and a good guy.
"We've got a press conference tomorrow so we can extol his virtues then."
Suarez's goal came when he received a neat pass from Dirk Kuyt before rounding Asmir Begovic and knocking it goalward and even though Andy Wilkinson got the final touch on it, Potters boss Tony Pulis was happy for him to have it.
"If I was Kenny, if he (Suarez) was half-a-yard anywhere near the ball I'd be saying it was his goal," he said.
"We are quite happy for the lad to have it.
"I watched him in the World Cup and in games for Ajax and he's a wonderful player - but give him a bit of time."