Hibs hit the woodwork twice through Fraser Fyvie and Scott Allan, but were caught with a classic counter-punch in the 75th minute when Craig Sibbald headed in a Blair Alston cross.
A clearly disappointed Stubbs said after the game: “There’s only one team who deserves to be in the final – unfortunately it’s not us (in the final).”
However, a riled Houston pointed to the fact that Falkirk have beaten their Championship rivals three times and drawn with them once in four meetings this season.
“After every game we’ve played against Hibs this season, they’ve deserved to win, according to Alan,” he said.
“What he should maybe think about is where we’re getting our goals from – crosses into the box. Deal with it. That’s what I would do.
“As a coach, I’d be saying to my team that we need to stop crosses because every time they put one in they score goals.
“Go back and look at the videos – they can’t deal with crosses into the box. I’d say that’s his problem and not mine.
“Rather than say only one team deserved to win he should think about how the team beat you.
“That’s three times we’ve beat Hibs this season and we drew 3-3 after being 3-1 down at Easter Road. So I’d be concerning with myself with losing goals, the way Hibs lose them to us.”
Houston continued: “Of course, Hibs were unfortunate not to win the match. I’m straight up on that. They put a lot into it.
“They hit the crossbar and the post. But we should have had a penalty when Botti Biabi was brought down – the fourth official Crawford Allan agreed with me on that. So it could have been 2-0 to Falkirk.
“They were the better football today but don’t disrespect us by saying we didn’t deserve to win – we put a lot into the match defensively.
“And the most important thing is that we scored the goal to win the match.”
The former Falkirk player, who guided Dundee United to cup victory in 2010, admitted a final victory with the Bairns would be a career-topping achievement.
“If the final can equal what I had in 2010 with Dundee United, it’ll be the best ever,” he said.
“I would never take anything away from that day as it was only the second time Dundee United won it in their history.
“Falkirk haven’t won it since 1957 so, with my connections, it would be a huge thrill for me to win it with this club.
“That’s why I came back into management. If it was another club, I’d have probably stayed scouting with Celtic, going all over Europe.
“But Falkirk gave me the buzz again. It would mean an awful lot to win it with Falkirk but I’d never disrespect or disregard the one with United.”
Houston would like Inverness to come through their semi-final against Celtic on Sunday.
He said: “We’ll have a better chance in the final if we get Inverness. No disrespect, but I’d rather have them and it could happen.”
Stubbs had no complaints about his players’ efforts but bemoaned a lack of cutting edge – and good fortune.
He said: “My reaction is the same as everybody else. It’s one of disbelief that we haven’t come through that.
“We controlled the entire game and that makes it worse.
“It’s the worst time to lose in a competition because you are so close but so far.
“I just wish we had some of the luck the opposition had today. We have to be more clinical. You have to take your chances.
“An element of that was down to the luck they carried. You can accept one coming off the post and back into the keeper’s arms, but when you have another you maybe start to think, ‘is it one of those days?”‘