Anthony Stokes fired Celtic to within touching distance of the first silverware of the season but refused to be drawn on their prospects of claiming a domestic treble.
The Hoops striker was on target with a double yesterday to set up a meeting with Kilmarnock in the Scottish League Cup final on March 18.
Boss Neil Lennon has already shrugged off talk of Celtic coming out on top in all three competitions this season and Stokes was reluctant to look beyond this weekend's Scottish Cup tie at Inverness.
He said: "I'm not going to talk about the treble. The gaffer has said enough about that. We are going to put the final on the back-burner now and just concentrate on the games that we have coming up."
Skipper Scott Brown opened the scoring from the penalty spot, before Jay Fulton levelled for the First Division side. Falkirk had already dumped holders Rangers earlier in the competition but hopes of an Old Firm double were dashed when Stokes netted with an impressive free-kick, before claiming his second of the day with five minutes to go.
He said: "I was delighted with the result and happy with the goals as well. We didn't take our chances in the first half but we made up for it in the second half."
Stokes was impressed by the opposition in the last-four clash at Hampden, with Falkirk's Kallum Higginbotham named man of the match.
The Dubliner said: "We did our homework and the gaffer showed us DVDs. We know what they are like, they try to play football and they did that today. Thankfully, we came out on top. We knew they were going to throw everything at us in the last five or 10 minutes but the third goal just killed it so it was nice to have that bit of a cushion."