Saints clinched their place in the Scottish Premiership top six in the absence of Wright, who is still in hospital after undergoing a gall bladder operation earlier this week.
Wright picked the team and tuned in by radio from his bed, listening as a Steven MacLean strike and an own goal from Ryan McGivern handed his side three vital points.
Davidson said: "I can barely speak. I've lost my voice!
"It was different today and I'm delighted for Tommy. He phoned me after the game, asking me why I'd made certain decisions. But he was delighted for everyone at the club.
"That's three times in a row we've been in the top six, which is a big achievement for a club like St Johnstone. The chairman had to cut the budget this year and we did cut a lot of costs, but we've managed to get there again.
"The boys just give Tommy stick but he'll be back shouting at them soon. I think he had the game on the radio. He shouldn't have been doing that for his stress levels, but he picked the team after we discussed it and I just passed on what he said.
"As a group of players we've got one goal - to get to the top six and do well in the cup competitions - so we're halfway there."
Hibs boss Terry Butcher had no complaints about the red card shown to Danny Haynes soon after they went 2-0 down but he was disappointed with their performance in front of goal, not for the first time this season.
"We changed the system round and for the first half I thought it worked very well. St Johnstone changed their system round to match ours, which is an indication that we were doing well," Butcher said.
"But from their first attack they scored and we couldn't then respond in the right way and Sean (Murdoch) has had to make another good save.
"But we've done well up until the box, again, and we've been powder puff in front of goal, again. I don't think Alan Mannus has had a save to make apart from a Frazer Wright header.
"I said at half-time 'let's go out and give 45 minutes of real effort' but we didn't start the second half particularly well, for whatever reason, and we conceded a very sloppy goal.
"Then the sending-off happened and it was game over really. I've got no complaints about the red card. I've seen it a few times now and I don't know why he did that."