Parkinson pointed to comments from Southampton chairman Dragan Solak, who said the Saints had “suffered enough”.
“They will move on and everyone else has to move on. I was reading the quotes from the chairman. They have been severely punished,” Parkinson said.
“They lost the chance to get into the Premier League. That’s punishment enough. Tonda is a young manager and I’m sure he’s taken responsibility.
“He’ll learn from it, but now everybody has to draw a line over it and move on.”
Wrexham’s Hollywood owners Ryan Reynolds and Rob Mac took a dig at Southampton last month with a promotional video aired ahead of league matches.
The Red Dragons won the encounter at the Hippodrome 2-1 thanks to an own goal at the death by Keven Schlotterbeck.
The win sent Wrexham into an extended international break and eased the pressure on Parkinson after their 6-0 defeat at West Ham.
But the three-time promotion-winning manager took three weeks without a Championship match, creating new problems for Wrexham.
“It’s been a long three weeks. It’s been a decent three weeks. The friendly against Wigan was really important,” said Parkinson.
“Three weeks is a long time for kids without competitive play. The only thing we can do is plan for three weeks, which we did.”
He added: “There were a few things that didn’t go our way, but everyone will get it in three weeks.
“Overall, I think the guys have trained well. They’ve had a decent balance between rest, fitness work and 11v11 training.”