Martin Boyle scored the only goal of the match in the 61st minute from 12 yards.
The winger was involved in the penalty award as his first-time shot was adjudged to have struck the arm of Jamie McCart, who was standing right in front of him.
McCart was booked over that incident and then received a second yellow card 15 minutes from time after sarcastically applauding the far-side linesman.
The penalty award ended up deciding a tight contest and Davidson admits it was a bitter pill to swallow.
He said: "I've seen it back - and I think my first reaction was correct.
"I didn't think Jamie's hands were in a position where he was making himself bigger.
"I think the ball basically came off his chest area. The guy was a yard away from him.
"So realistically, I'm not quite sure.
"It's disappointing because both teams were having a real go to win the game.
"To end up losing the game to that decision is quite hard to take, quite frustrating.
"I think it's really hard for the referees sometimes. For me, they've just got to be sure it's a penalty.
"It would be different if Jamie's hands were up high or trying to block the ball.
"As a defender, and I'm sure Jack will say the same, I'd be disappointed to lose a penalty like that.
"I think it's just very unfortunate how it's affected the game."
The result leaves Hibs just one point adrift of cinch Premiership leaders Rangers ahead of next Sunday's clash at Ibrox.
Boss Jack Ross, whose team had lost their last four games to Saints - including the Scottish Cup final - said: "To go into this (Rangers) game at that stage of the season as a top-of-the-table clash is indicative of how we have grown as a team.
"We just want to keep doing it, there's nothing wrong in keeping striving.
"When I said it was a game to look forward to, it's because we go there deservedly as a team who are second in the table and only a point behind.
"The incentive is for us to beat the champions at home and go top, and it's a brilliant incentive.
"It's not one or two games into the season, we're into a decent part of the season now.
"We've had one defeat all season and that was with 10 men for the last half hour.
"So we have got a good team and they are finding different ways to win games.
"I thought earlier in the season we were really at it, we've had to dig in a bit over the course of the last weeks but that's the sign of a team that keeps growing."