Still plenty of room for improvement, but Hearts are on the right track, according to head coach Robbie Neilson.
The Jambos delighted a sold-out Tynecastle crowd with some scintillating football in a sizzling first-half display that saw them head into the break three goals up.
A Jordan McGhee header and a Billy King double put Hearts 3-0 up before two late goals from either side, including an Osman Sow spot-kick, made the final score 4-1 to the home side.
After the match, Robbie was full of praise for the display his men put in during the first half rout of the Bairns, but revealed the team's performance in the second half gave him plenty to think about for the future.
"I thought we played really well in the first half, and we should have scored a lot more than we did. Peter Houston changed his shape at half-time, and we got a bit sloppy. When you come in 3-0 up at half time it can be a difficult score line, because the players can think the game's won.
"The first fifteen minutes were fine, but then the game got a bit flat. I've been saying goal difference could be crucial in the league this season, so to lose a silly goal like that was really disappointing, but ultimately the win is the most important thing."
A black mark on the day's proceedings saw Prince Buaben spoil an otherwise outstanding personal performance with a red card for what referee Kevin Clancy deemed to be a dangerous tackle. The gaffer was reluctant to discuss the incident in too much detail until he'd gotten another look at it.
"From my perspective, I thought it looked a strong tackle, but also a fair tackle. We'll just have to deal with it, though. It's disappointing if we're going to lose Prince but that's where we are. I'll have to speak to him about when the best time is to make a tackle like that. If you're 3-0 up, maybe it's not a challenge you need to make."
In addition, Robbie had words of praise for the attacking verve his side showed, and reserved special acclaim for James Keatings who, despite missing a spot-kick in the first half and being denied another hat-trick by the outstanding Jamie MacDonald, put in the kind of display Robbie wants from his whole team.
"Today the boys did a lot of things we've been working on. They got the ball wide, they passed and moved, they played through the centre of the park and got forward at pace. They didn't do enough of it in the second half, they took too many touches at times and invited Falkirk into the game, but at least it gives us something to work on in training.
"James was fantastic today. He didn't get a goal but his movement was top class, and Jamie MacDonald was superb in goals for Falkirk. We know how good a shot stopper he is, so credit to him. James is disappointed he never took any of his chances but other things he brought to the side were great, so he can be very happy with himself."
Finally, Robbie admitted he had intended to give Soufian El Hassnaoui his debut towards the end of the match, but circumstances dictated that Soufi would have to wait for his chance, and revealed Alim Ozturk was substituted purely as a precaution due to his hamstring tightening up a bit, with the game already won by that point.