Houston’s comments came after Falkirk’s 1-0 victory over Hibs in the semi-final of the Scottish Cup on Saturday.
The Bairns manager was not pleased when Stubbs claimed the Edinburgh side deserved to win the match, pointing to the fact that his team have beaten Hibernian 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,” said Houston.
“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 myself with losing goals, the way Hibs lose them to us.”
But Stubbs – whose side have already clinched a place in the Championship play-offs, while Falkirk have two games to claw back Queen of the South’s five-point lead for the final slot – produced a withering response.
Stubbs said: “Peter is entitled to his opinions. He is a very experienced manager who has been there a long time. I’ll take his words on board – thanks for that.
“Look at the table. We’ve scored more goals than the rest of the teams. We’ve got a better goal difference than the rest of the teams. So we’re not doing too bad.
“I’m thankful to Peter for pointing this out to us. I’m always looking to learn.
“Obviously he’s been around a lot longer than me and I’m in my first season as a manager. We’re doing okay.”
Asked if the row might add spice to their next meeting with the Bairns at the Falkirk Stadium on the final day of the season, Stubbs said: “It might do. We’re focusing now on going up in the play-offs. So we’ll just concentrate on that.”