The new boss got off to a winning start as the Minstermen beat Brackley Town 2-1.
Parkin got two goals, one a great free-kick, to give Gray the first game he wanted since his switch from Darlington last weekend.
The veteran targetman thinks his arrival gave everyone a lift.
“It’s been good,” Parkin told the National League’s Oli Osborn after the game. “Training has been enjoyable. It’s obviously always a change when a new manager comes in he will want to bring his own ideas in.
“Over the next few weeks and months we are going to understand more of what he wants from us and we will take it on from there.
“Promotion is still the main aim. That’s the reason why I re-signed in the summer - I want to get this club back to where it should be.
“It’s a massive club. With the fan base that we have got it’s not really a club that should be in this league - but we are in it and it’s our job to now get out of it.
“We are probably six or seven points short of where we should be at,” Parkin added.
“I’m pleased with my season so far personally I’m at the back end of my career now so it’s not about how I am doing. It’s about the club and getting back up.”