St Johnstone rage at 'horrendous' decision in St Mirren defeat as key player dislocates shoulder
Greive added a second goal for St Mirren early in the second period, sending St Johnstone bottom of the table in the process.
Davidson said: "I was disappointed with the penalty given against us. It was a horrendous decision.
"I've watched it back numerous times and I'm still to see it. He said it was a blatant shove to push the player down. To me the ball was waist height, the player tried to head it and Jamie was behind him.
"Big decisions in games can change it especially when confidence is fragile. I sound like a broken record but huge decisions have cost us so it's hard to take especially when confidence isn't high. These things have to go for us."
Davidson, who revealed midfielder Cammy MacPherson dislocated his shoulder, also admitted his team had not responded well to the setback.
He added: "I told the players I want them to fight and encourage them to play and believe they are good players and to do the right things. For 25 minutes of the second half we didn't do that."
The win carried St Mirren into the top six and within a point of fourth spot, to the delight of manager Jim Goodwin.
He said: "This is where we want to be. We've spoken about it over past seasons about putting us in the mix for the top half.
"We've got a game in hand and if we win that it'll put us into the scary position of fourth which would be incredible at this stage. But we can't dwell on the win.
"We have to recover properly for the weekend. As it's so tight and congested we can't get carried away as you could quickly go back to ninth or 10th. We need to remember why we are on the good run and it's down to hard work."