The Perth side played most of the second half two men short after Chris Millar was ordered off, joining Steven Anderson, who was shown the red card in the first half.
But despite the numerical advantage, the Paisley Saints had only Paul Dummett's goal to show for their efforts as the visitors held out for a share of the points thanks to Murray Davidson's early goal.
With St Johnstone boss Steve Lomas serving a touchline ban, assistant Wright was in charge in the visiting dugout. And he revealed he was very proud of the way his side battled to stay in the game.
"We worked really hard, but nothing surprises me about these players even after we went down to nine men," he said.
"We were truly terrific keeping it down to one goal and I am really proud of them."
St Mirren laid siege to their opponents' goal in the final 20 minutes and Alan Mannus had to be at his best to keep them out.
Wright added: "The keeper was terrific and a bit unlucky at the goal after pulling off a great save from the first shot. But he would be the first to thank the players in front of him and Frazer Wright's goal-line clearance and the block by Tam Scobbie typified the spirit."
The assistant boss had no complaints about the two red cards, saying: "For the first red Stevie Anderson's the last man and, although he slipped, you can have no complaints.
"I think Chris Millar also slipped for his second booking, but when you are already on a yellow card you need to be careful."