The celebrating manager says he will pull out all the stops to prevent them becoming a yo-yo club.
He doesn't think the step up should stop them playing with the attacking edge that has served them so well in the past three years.
Back in November, his side were sitting in 18th place in the Vanarama National League North. With just 13 points on the board, they were just four points above the drop zone.
During that low-key start, Alty got tonked 5-0 at Boston United.
On Saturday, the Robins returned to the scene of the crime and put the record straight to earn their second promotion in three years.
“I would like to think we have never let the fans down - we have changed the culture here and hopefully we can continue that,” he told AltyTV.
“We don’t want to stop and stand still now. We don’t want to be a yo-yo club, that’s for sure. But to establish ourselves we know it is going to be very difficult.
“We are going to have to improve in every area at the club, including on the pitch.
“It will be a big challenge but we want to keep on building.”
With a 1-0 win, Alty regained the Step 1 place they lost in 2016 - a tumultuous time which saw them again relegated a year later.
Parkinson arrived alongside Neil Sorvel and in 2018 they won the NPL Premier. On their North return, they finished fifth but lost in the play-offs.
Alty went one better at York Street on Saturday and another party was started.
“It was extremely tense but we always stayed in the game,” he added. “Boston had a game plan, but we stayed strong and gave ourselves the opportunity.
“We weren’t impressed with our first half performance but we managed the game well after we went in front.
“Finals are about fine margins. Dan (Mooney) took his goal superbly, he had done his research and knew their goalkeeper had done something similar in the past.
“People will think I’m crazy but I truly believe if we had a better start to the season, we would’ve won the league this season.
“We know the step up is a big one and we’re going to have to be ready.”