Already without four self-isolating players before Sunday's semi-final win against St Mirren, Davidson only had a 16-man squad for their 4-0 defeat at Celtic Park with Zander Clark, Liam Gordon, Michael O'Halloran and Ali McCann dropping out.
Davidson will now seek more guidance to ensure they do not suffer any more blows before they face Hibernian on May 22.
"It's very concerning," he said. "I think the whole world is concerned about Covid, so it's not just me, but it's not a nice situation to be in.
"We're doing our best with everybody, we're not experts on it, so we're trying to get as much help as we can to make sure we're all safe.
"We followed Government guidelines and it's paramount we keep them safe.
"We'll get three or four of the players back tomorrow (Thursday), which is great, and the good news is that they're all asymptomatic, so they are not suffering at all.
"We must try to stamp it out and we can't let it fester until next week."
Davidson is still hopeful he will have a full squad for Hampden minus the injured Scott Tanser.
"That's why we're trying to shut the place down as much as we can and test people as often as we can to make sure everyone is safe," said Davidson, whose side remain fifth in the Scottish Premiership, ahead of Livingston on goal difference, before their meeting on Saturday.
"Fingers crossed. But what this last week has taught us is that it's a difficult virus, and that's why we're all in this pandemic."
Saints are hoping to get back into training on Thursday.
"We'll go over the guidelines with the Government and follow their instructions to the letter to make sure we're prepared," Davidson said.
"It will probably be socially-distanced training, but it's important to get the players out on the grass as quickly as possible."
Celtic's win proved a fitting send-off for Scott Brown in his last home match and the Aberdeen-bound skipper set up their second goal with a long diagonal ball to Odsonne Edouard.
David Turnbull had opened the scoring 60 seconds earlier and both Kristoffer Ajer and Karamoko Dembele netted in the latter stages.
Interim manager John Kennedy said: "That was the motivation for us, when you come to the end of the season and there's not a lot to play for, that was easy for us with Scott leading the team out for the last time at Celtic Park.
"It was important we put in a performance that sent him off in the right manner, which we certainly did.
"The plan was, because we have a quick turnaround until Saturday, he knew he would come off after 60 minutes regardless.
"But the saddest thing was the stadium wasn't packed to the rafters with people singing his name the whole game. But that's the world we live in.
"But there was the staff and players and an element of the support outside to send him off. It's probably the best of a difficult situation.
"In the last few days he is starting to take it all in, I have seen him spending more time around the offices and speaking to more people, and it's probably now in his final week it is hitting home that he has to cherish what he has got left.
"We will cherish every moment we have got him for the final few days for what he has done as a player and captain for this club. We have to be grateful and hopefully send him off in the right way on Saturday."