The Perth side face Cowdenbeath in the Scottish Cup on Monday night after the fourth-round match was rearranged following a second postponement.
While the full focus for 90 minutes will be on getting three SPL points, Davidson accepts St Johnstone will have to begin preparing for the cup tie as the final whistle blows.
Despite the fifth round being almost two months away, cup rules mean the game is to be played on Monday after a second postponement, and Cowdenbeath have been handed a possible advantage after their Irn-Bru First Division clash with Partick Thistle was postponed.
Davidson said: "It's not ideal. It's probably the first time in my career that I've done it.
"I know myself, and a lot of the boys - on the Sunday you feel okay and the Sunday comes and you feel a lot more stiff.
"So as soon as the game finishes on Saturday, more than any other game, we have got to make sure we are doing the right things to get ready for Monday. Ice baths, eating right, drinking right, getting everything back in your body to make sure you are as close to 100 per cent as you can be.
"There is nothing we can do about it and we have to make sure we are as best prepared as we can be.
"It doesn't matter if it's Tuesday or Wednesday - you have got to prepare right, but obviously being Monday it's going to be tough.
"There has to be a reason for it being Monday - I'm not sure why. You have got to just accept it."
Manager Steve Lomas added: "It's a strange one. I have never heard anything like that before.
"You would have thought Tuesday night would have been ideal, but I don't know what the rules are.
"It does seem strange when you have got a free week that you put it on the Monday, 48 hours after a game.
"It will be a challenge, two away games, and Arbroath did brilliantly at Celtic Park so they will fancy their chances of causing an upset.
"It's a tough couple of days but it could be a good couple of days with two wins."
St Johnstone will face another trip to Paisley in the fifth round if they beat Cowdenbeath and Lomas expects to face a St Mirren side desperate to continue moving forward following a six-game losing streak. Danny Lennon's team are now unbeaten in three.
Lomas said: "They are probably looking at it like us. After the first five games we probably thought we should be sitting on eight points rather than the two we had.
"That's football. It all boils down to the two different ends of the pitch.
"Can you keep them out and can you take your chances when you get them? They are the small margins."