The former Newcastle striker earned a yellow card for diving in the first half when, after rounding Magpies keeper Tim Krul, he went to ground in the penalty area.
"I don't think it was a penalty but neither did I think Andy was trying to get a penalty," Dalglish said after the game.
"The decision not to give a penalty was correct but it was harsh to show him a yellow card, he was always struggling to keep his balance.
"We had chances and we were unfortunate not to get a penalty, and that would have left us playing against 10 men," he added.
"Then they got the goal, which from our point of view was disappointing, and the boys showed frustration and maybe started feeling sorry for themselves.
"Pepe got frustrated and got himself a red card and Andy marched up the tunnel. He was frustrated and disappointed for himself and at the result.
"There's no problem with the red card for Pepe but there is a problem that we never had a penalty kick."