Black Cats defender Lynch collided with team-mate Jon McLaughlin late in the second half of Pompey's 2-0 victory at Fratton Park, although Parkinson said he was pushed by Harrison.
The stretcher was called for almost immediately and Lynch was taken out of the ground to hospital.
Parkinson confirmed the centre-back was knocked unconscious, but did come round before leaving Fratton Park.
Nine minutes of added time were played at the end of the match, largely as a result of the delay in play caused by the injury to Lynch.
Parkinson told the Sunderland Echo: ‘He was knocked unconscious and has gone to hospital.
‘We don't really know the extent of his injury yet and we just hope he’s alright.
‘The centre-forward (Harrison) has just pushed him (into the goalkeeper), there’s no need for him to do that.
‘It looks like he has suffered a very bad injury and it is a worry when someone is knocked clean out.’
A goal in either half from Christian Burgess and James Bolton earned Pompey a club record-equalling eighth successive victory and moved them up to sixth in League One.