The midfielder pulled up sharply midway through the first half after playing a pass and was promptly replaced by Charlie Adam.
Dalglish confirmed Spearing was suffering from a tight hamstring, but he's optimistic it's not too serious.
The boss told reporters: "It was his hamstring, but it wasn't too bad. It just went a bit tight on him. I don't think he has pulled anything, but we'll have to wait until the morning when he gets back (to Melwood)."