Parkinson is fighting for his life after suffering a stroke.
Adam gave the visitors a 45th-minute lead from the penalty spot.
Adam, who dedicated his strike to Parkinson by producing a t-shirt bearing the message "4 Parky", sent keeper Steve Harper the wrong way from the spot after Luke Varney had been tripped by Alan Smith.
Blackpool headed home hoping to hear better news of Parkinson on their return, but with their manager Ian Holloway having had football put into perspective once again.
He said: "We will find out a bit more in the next few days, but they are a very important few days and all our love is with him.
"I can't talk about it at the moment, but it is very serious. We believe in him and his family.
"All our love is with him and we believe he will come through it."