After their demoralising last-gasp loss to First Division outfit Ross County in Tuesday's Scottish Cup quarter-final replay, John Hughes' side bounced back to regain fourth place in the SPL.
The visitors certainly had their moments of good fortune as the Bairns twice hit the bar through Enoch Showunmi and Darren Barr, but Hibs held on for a vital triumph.
Riordan, who netted his 15th goal of the season with a sublime free-kick to quickly cancel out Mark Stewart's opener, said: "It was an important win.
"The gaffer has talked to us about the stupid goals we have conceded. If you look at those goals in the last six or seven games, like at Hearts last weekend, they have all been scrappy goals against us, maybe our own fault, silly errors.
"It's something we need to stamp out and we did that.
"We defended well, big Sol (Bamba) was great and I think we deserved the win.
"It's been frustrating our run, but we got the victory.
"We needed it."
After Riordan levelled, further goals from Anthony Stokes - his 19th of the campaign via the aid of a deflection off Tam Scobbie - and a Bamba header virtually sealed the victory before half-time.
The bottom-placed Bairns will play worse and win, but Riordan knew the result was all that mattered as Hibs stayed two points behind Dundee United ahead of their potentially-pivotal meeting in Edinburgh on Wednesday.
The Scotland striker , 27, added: "I was just delighted to get the points obviously, that was our main target.
"I think we held on towards the end, they had a few good chances across the box but we got away with it.
"Wednesday will be a tough game. United are a good, strong, physical side, a hardworking team.
"They have just put Rangers out of the cup as well. We are battling with them for third, we have been for a while now, and we've just got to try and take as much as we can out of the game."
Falkirk defender Marc Twaddle felt his team deserved far more from the contest.
The Bairns, who remain four points behind second-bottom Kilmarnock, took the lead for the fourth game running but have failed to win any of them.
Twaddle senses the tide will turn and the left-back added: "I really don't know what to say. We outplayed them and were beaten 3-1.
"We lost three sloppy goals but we created numerous chances and just couldn't put them away.
"But we'll take the positives. We could have gone under after playing so well and going in 3-1 down at half-time.
"We could have felt sorry for ourselves but we created a lot of chances in the second half."
Source: Team Talk