Tidser had a scan on a persistent knee problem last week but has been forced to wait for the results, while di Giacomo is struggling with a freak back injury.
And Ton boss Moore believes he will have to be patient before he discovers how long the pair are going to be out of action for.
Moore told the Tele: "Tidser was meant to get his results back yesterday but when we phoned up we were told the surgeon would be away on holiday for the next two days.
"That is something we weren't expecting so we still don't know the result of his scan yet. That has dragged on a couple of days longer than we thought.
"We will know a bit more about Paul di Giacomo's injury in the next couple of days and we will wait and see if he can get back in to train.
"He was feeling his back a little bit on Friday morning and didn't do as much training as the rest of the boys but we didn't think much of it.
"But on the Saturday morning he said his back was agony. He couldn't move and couldn't kick the ball so we left him out.
"To be honest I had something similar about two months ago when I got up and my back was in agony, but it went away after two or three days.
"We're hoping that it is just a trapped nerve or something and he will be fine to get back training but we will have to wait and see."
And the Cappielow gaffer also has a serious concern over captain Stuart McCaffrey - who reported for Monday's training on crutches.
He said: "Stuart McCaffrey is going to be struggling for the game against Partick Thistle on Friday.
"He has inflammation on the bottom of his heel. He has been carrying it for a few games but he thought he would be fine.
"He thought he could get to the international break and rest it, but he came in on crutches on Monday so I don't think he will make it."
Meanwhile, Ton went down 4-2 in a bounce match with SPL side Motherwell yesterday - with Archie Campbell grabbing a first-half double.
And despite the defeat Moore was full of praise for his side, with a number of players singled out particularly.
Moore said: "We had a bounce game at Motherwell up at Dalziel Park and it was great - the first half we were really good and played some excellent football.
"Archie Campbell scored two good goals, and he and Peter Weatherson did really well up front together.
"Darren McGeouch and wee Fred did well in the middle of the pitch and wee Sean Fitzharris did well again out wide.
"We gave Andy Graham and Ross Forsyth 45 minutes, Kevin McCann and wee Sean 65 and big Peter and Archie got the full 90.
"The new keeper we brought in from the Juniors, Matthew McGinley, got a game and did okay, he made a few good saves in the first half.
"We ended up getting beat 4-2, but we brought a few of the under-19s with us and they came on for the second half and we lost a bit of rhythm."