Chris Herd put the visitors ahead in the 10th minute and it took until the 82nd for the Reds to equalise through Luis Suarez's close-range header.
Dalglish was unhappy with two penalty appeals which were turned down by Oliver and also the official's decision to later book the Uruguayan for diving.
"I have never heard of a penalty not being given by a referee who said the boy was unlucky - what chance have we got?" said Dalglish.
"He didn't give it (the penalty) but he said to Dirk Kuyt the boy (Lichaj) was unlucky. I can only tell you what they were saying in the dressing room - don't ask me to justify it.
"When you consider the penalty was refused because the opponent was unlucky, it just doesn't add up.
"Dirk takes it on his chest to go past him, the guy knows he has missed it and he has (spread) his arms and he (Oliver) said he was unlucky - I think Dirk Kuyt is unlucky.
"Even Suarez's booking, the guy has trodden on him and it is a joke. You can imagine the headlines - he got booked for diving and the guy (Stephen Ireland) has actually trodden on him and he is lucky he has not broken his foot.
"And Hutton was a bit fortunate in the first half."