St Johnstone handle heat to relegate Dundee - as Aberdeen boss Jim Goodwin fumes at display
Hendry latched on to Glenn Middleton's cutback to settle the contest and, in turn, relegate Dundee, who had been given renewed hope following Tuesday night's 3-1 win over Hibernian.
Davidson was full of praise for the way his players dealt with any added nerves following that result, and said: "I think last night's result put a lot of pressure on us.
"Some people were saying we were definitely in the play-off, but with Dundee winning by a couple of goals, this was a game where we had to perform under pressure.
"I was really disappointed in losing to St Mirren (at the end of April) that under pressure we couldn't do it, but we did it tonight and took a big step forward going into the play-off games, having that belief in each other that we can perform when we need to.
"We've got a few knocks and niggles and a few boys are near suspension as well, so we'll need to assess the squad on Friday and take it from there, but the main focus is we've got 180 minutes of enormous football ahead of us.
"We want to stay in the league, we're desperate to stay in the league and I think you saw that tonight."
He said: "I'm extremely disappointed with the end result and the overall performance. I think the game as a whole just about sums up how the season has been really.
"We've had plenty of possession again tonight but just weren't able to do enough at the top end of the pitch to cause St Johnstone problems.
"The goals that we've conceded since I've been in and prior to that have been far too cheap and we found ourselves chasing the game again.
"St Johnstone are a notoriously difficult team to breakdown and I felt tonight we probably could have played for another two hours and not scored a goal - that was the feeling I had, so I'm extremely disappointed and we'll just need to take it on the chin.
"I had hoped that when I came in I would get a better reaction from the group. I had hoped that we would get that bounce.
"I still felt there was enough time left to do that, so I have to take responsibility for that - I wasn't able to get the kind of reaction I had hoped for, hence we find ourselves in the situation that we're in.
"It's been an extremely challenging and difficult couple of months since coming in, but we know what we have to do in the summer, we know the improvements we have to make, we know that a number of players are going to be leaving the club and it's up to us now to make sure the players that come in are better than the ones that are leaving."