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.
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."