Last midweek, the Bairns lost out 1-0 to SWPL2 side Stirling University away from the home.
A victory in the tie would have set up a glamour tie against SWPL1 champions Glasgow City, but Muir said it just wasn’t to be on the night.
He said: “We defended really well and limited the amount of clear-cut opportunities they had down to not very much.
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"They had most of the ball but we had decent chances, one of them at 0-0 in the second half was one we really should have taken.
"It was funny because we defended behind the ball so well and their goal was the one moment in the game we got caught up the pitch a little."
He added: “I was really proud of the desire and effort the players put against higher league opposition, they made it a competitive tie.”
With only three games left of the SWF Championship South season, he is hoping to lead the side to as high a finish as possible.
The Bairns currently sit top of the bottom-half split in the league, one point above Airdrie.
Muir said: “The way it has worked out with Clyde withdrawing from the league, it's led to us to only having three games left.
“We didn’t play on Sunday there and we have another week off in there due to another team dropping out earlier in the year.
“Our goal is to finish as high as we can in this bottom half of the league and we hope that would then give us a kick-start for next year.
“The three teams we are playing, we have beat them all this season but it isn’t as simple as that.”
All three matches will be played at the Falkirk Stadium, and Muir believes it doesn’t actually serve as much of an advantage.
"We’ve probably performed better away from home this year,” he said.
"It's crazy the way it has worked out and I am not sure how they managed to actually work it out like this.“We’ll try to make it a positive for us because we should enjoy being at home.”
Falkirk next face second-bottom club BSC Glasgow on Sunday afternoon.