Carlo Monti also saw red for Morton and both players will now be suspended for tonight's league match away to bottom club Stirling Albion.
After the weekend defeat to Falkirk, Ton boss Moore opted against facing the press as he did not want to be drawn on the display of ref David Somers.
Moore told the Tele: last night "I knew I would get questions about the referee and I thought I might get myself into trouble if I came out so I decided against it.
"With Michael Tidser's red card, I am disappointed with him, not the referee.
"He gave him a booking for mouthing back and he should have kept his mouth shut and got on with it.
"The red card I disagreed with was Carlo Monti's. I don't think there was any malice in it - it was a mistimed tackle.
"The only reason he has given him a red card is that the fans up in the stand have reacted.
"The amount of bookings the referee dished out was unbelievable, considering there wasn't a bad tackle in the game."
And Moore has warned Monti and Tidser they face a real battle to get their places back.
He said: "Obviously when we go up to Stirling Carlo and Michael can't play, and I've told them they could be out of the team for quite a while as we've got everybody back.
"If we go up to Stirling and the boys win then they could both find themselves sitting in the stand or on the bench for quite a while."
Tonight's match heralds Moore's return to the league's bottom dogs for the first time since swapping the club for Cappielow in the summer.
But while he is looking forward to making the visit, Moore insists he is only concentrating on getting the win.
He said: "It will be my first time going back there since I left and I'm looking forward to it - although I will enjoy it even more if we get the three points.
"I'll do the hellos after the game. Before the game is over and done with, I'll be professional and concentrate on our team and make sure we come away with the three points.
"It's not going to be easy though, and they proved up at Ross County at the weekend that they are no mugs. But at the same time we've got to make sure we up there and get the three points.
"Looking at their team on Saturday they have good experience. Players such as Ross Forsyth are back playing and he is a massive player for them.
"They've also got Gordon Smith who is one of the league's top goalscorers, so it's not going to be easy."
Moore, pictured, will be forced to alter his midfield, with Monti and Tidser both suspended, but Derek Lyle has recovered from a head knock to leave him a fully fit squad to choose from.
Moore added: "Derek is fine, it was just a knock on his head. Darren Young also came back in on Saturday and Sean Fitzharris will be involved again."