The Scottish Premier League's bottom club closed the gap on Killie to one point but manager Eddie May will not treat the cup campaign lightly just because his team are involved in a relegation battle.
"It's another game we need to go and win, and hopefully not draw because I don't fancy playing on a Monday and Wednesday," May said.
"I can't understand the ruling but I don't understand why they don't play reserve games either. But that's for the authorities to decide and we will just look for the win.
"Do you make a preference towards the cup or the league? I don't think you do. You've got a commitment to every competition.
"Footballers sometimes get it a little bit easy, so let's go and work hard. If we've got a replay on Wednesday, we'll work extremely hard.
"So we'll look forward and not worry about how many games we have to play. The more games you have, the more successful you are."
Twenty-four hours did not prove enough time for Jimmy Calderwood to lift Kilmarnock as his first match in charge ended in a 3-0 defeat by Motherwell.
But May has first-hand knowledge of the motivating factors of his former Dunfermline manager.
"He'll definitely be different from Jim Jefferies, I have played under both of them," May said.
"They are different characters completely and two very good managers. I'm looking forward to it, the first time I have competed against him as a manager.
"He was very good to me when I was at Dunfermline and he did a very good job there.
"He is very positive and very honest - and he gave me a game as well, which helps."
May is quickly finding his feet in management after debutants Colin Healy and Enoch Showunmi helped the Bairns to their second point against Celtic this season.
The pair are ineligible for the cup tie while Darren Barr and Carl Finnigan are both suspended but May has increasing confidence in the depth of his squad.
"There has been a big shift in terms of team mentality and quality from the start of the season," May said.
"We have got more toughness. People were saying we were virtually an under-21 team but I don't think we're that now. We have better competition.
"It's only an opportunity, we are still bottom of the league. But if that's the commitment and quality we can get, I think we have a chance to get off the bottom."
Kilmarnock 11/10, Draw 12/5, Falkirk 12/5
Source: Team Talk
Source: Team Talk