Reid said: "It's a home tie which is the first thing, but our record v Falkirk in recent seasons has not been the best as we are aware.
"However, we cannot ask for any more than another First Division side at home, which therefore gives us a great chance to go for the semis.
"Falkirk will, of course, feel the same. What I do ask for is for all our fans to come out and support us that day, as Falkirk will bring a good support through, and we need everyone at Accies right behind us that day."
Second-half goals from Stevie May and Jon Routledge earned Accies a 2-0 win at East End Park as they saw off their Irn-Bru First Division rivals.
Victory in Fife continues Hamilton's recent purple patch and Reid was delighted with the backing his boys received from the stands.
He added: "The crowd we had and the support we had behind us was incredible, I couldn't believe it to be honest.
"It made a huge difference to the players. The players were astonished.
"It was a huge backing in terms of numbers for a team like Hamilton Accies and I think the team performed.
"The first half was pretty even but in the second half I thought we played some super football and scored two super goals."