The Portuguese midfielder left the field clutching his shoulder after coming off second best in a challenge with Grecians defender Danny Coles after just 19 minutes.
Dalglish does not know exactly how long Meireles will be out for but said: "Raul has hurt his collarbone. I don't know what the technical term is but he fell heavily.
"He will come back with us and we will see how long it is before he is back.
"We don't know how serious it is but it'll be a few weeks."