Tisdale said that Parkin's performance overall was superb and was delighted that he could cap it with the winner.
"Sam was outstanding on his debut. He really had a terrific game," Tisdale told Sky Sports News.
"Other than the goal, which is a major part of the game, his overall performance allowed us to get up the field and get into the opposition half.
"He offered a real challenge to the Rovers defenders and I don't want to ask too much of him too soon, but he showed that he is certainly capable of playing a game for us that is very, very important."
Danny Coles scored Exeter's opener, with Eliot Richards equalising for Rovers.