The 24-year-old Uruguayan doubled the home side's lead after a Roger Johnson own goal had opened the scoring.
"It was a fantastic goal for Luis. He has been fantastic since he came here," said Dalglish.
"He is playing with a wee smile on his face all the time and he is a good personality to have in and around the place.
"On the pitch, he has made a fantastic contribution. We are fortunate to have him and we look forward to a lot more happy days with him."
The Anfield boss also believed that his side were deserving winners on a day which saw them rise to fifth place in the Premier League table.
"It was a difficult game. I think it was an entertaining game. I think we deserved to win," he added.
Liverpool's next match is the Merseyside derby against Everton next Saturday.