He was proved right after Alty ran out clear winners over Chester on Saturday - that after a resounding 6-0 win at Curzon Ashton the week before.
After starting the day just a point ahead of the Blues, Parkinson said it was nice to stretch their lead with a win.
"They were one point behind us but the win gives us that little bit of breathing space now," he told the club's video service.
"We need to open up that gap even more if we can because Bernard and Jonno are a very good management team and they won’t be accepting that.
"I said at the Spennymoor game when people were starting to get a little unsettled and we lost – I knew we would bounce back, I knew were starting to play again."
After previously only seeing one win in their last six home games, Parkinson praised the fans for sticking with it.
He said: "We know it’s hard when we lose because of the expectation.
"The fans were brilliant today, my son was here so I wanted him to experience them in full flow.
"It’s amazing here when you win. It’s the best feeling in the world, I can’t explain it to people."
PHOTO CREDIT: Michael Ripley