And, ahead of their second meeting of the Irn-Bru First Division season tomorrow, the Ton manager knows his side must live up to expectations as they bid for a place in the SPL next term.
Moore's men are currently third in the standings, and the Greenock gaffer said: "You are always under pressure at Morton because the fans expect you to be top of the league.
"In fairness to the chairman, he wasn't too happy with us after the Hamilton game where we drew 1-1. He kept getting this thing into his head that we were playing with one up front, which I couldn't understand because when we beat Kilmarnock 4-1 in a pre-season friendly he said it was the best football he had seen and that this three up front was great.
"As soon as you get a bad result, it is back to one up front! That is the way the chairman interpreted it, but I have never played one up front in my career; it is either 4-4-2 or 4-3-3.
"I felt we were playing some good football then, but unfortunately, against Hamilton, we lost a goal against the run of play when we should have been three or four up.
"They got a goal back with 10 men and that was the catalyst for him being annoyed.
"Queen of the South put us out of the cup the week before and these are things that annoyed the chairman.
"I said from the start that we have got a squad that can be up there challenging, and if we are not up there, then I will be disappointed."