After guiding his side to a 1-0 win over Raith Rovers on Saturday that kept the Ton five points clear of nearest challengers Partick Thistle at the top of the Irn-Bru First Division, the Cappielow boss headed to Tayside to see the Dees and Kilmarnock play out a goalless draw.
Moore's men will put their promotion bid to one side when they head to Dens Park on cup duty this weekend.
And the Greenock gaffer, who will be without new signing Colin McMenamin, is hopeful they can cause a shock if everything clicks into place.
He said: "It was good to give Colin his debut on Saturday. We changed things about at half-time and went 4-4-2.
"We were struggling to get up the pitch in the first half because Laurie Ellis and Simon Mensing were playing well against Peter MacDonald so we took Davie Graham off because we weren't getting our wide players on the ball enough and went with the two up front.
"Colin won't be involved this weekend because he is cup-tied so that will give the two Peters another chance to play up at Dundee.
"We are going to have to ride our luck a bit, there is no doubt about that because they are an SPL team.
"Hopefully we can carry a bit of luck and get through to the next round.
"We had a good record up there last year when they were in the First Division so hopefully we can continue that on Saturday."