A Roger Johnson own goal, diverting in Charlie Adam's shot, and another magical Luis Suarez strike gave the Reds a comfortable half-time lead in Saturday's Premier League encounter.
However, Steven Fletcher pulled one back early in the second half and despite creating - and missing - a number of good chances, the home side were grateful for the final whistle.
"I think it deserved three points, although it was difficult at times," said Dalglish.
"They put us under a bit of pressure in the first half and then scored early in the second half which gave them a bit of momentum.
"We had a few headers and blocks to make but at the other end we broke away and hit the bar twice and their goalkeeper made an unbelievable save from Luis.
"We maybe got a bit of good fortune with the first goal with it coming off Johnson but I think we deserve a bit of luck because we haven't had much recently.
"We will continue to plod on and with a bit of luck in the second half, with the two that hit the post, we could have had another couple.
"We have got three points, we may get the luck some other day when we need it."
Suarez was again the side's stand-out performer, often tying opposing defenders in knots, and it was his intelligent movement and brilliant finish which brought the all-important second goal.
"Suarez has been outstanding since he came to the club," added Dalglish.
"We are very fortunate to have him and we look forward to many more happy days with him because he is a fantastic footballer."
Wolves boss Mick McCarthy was disappointed his side allowed a positive start to fade quickly but drew heart from their response after the break.
"We had a difficult first half and an excellent second half," he said.
"I thought first 10 minutes we started okay but then we conceded a goal, for which I thought Roger Johnson was fouled by Carroll and I was annoyed about that.
"The second one we tried to play offside and did it badly and it cost us.
"My goalkeeper is excellent and he has had a good performance but we were a far better team in the second half and that is the level of performance I would expect from us."