Hibs' fragile confidence was set to be sorely tested after their cup loss at Ross County, but just over a minute later they were back on level terms when Derek Riordan curled home a superb free-kick.
Poor defending from Pressley's side then allowed Anthony Stokes to fire his 19th goal of the season, with the aid of a deflection off Tam Scobbie, before Sol Bamba effectively sealed the points before the interval.
Pressley said: "In terms of attacking play, opportunities created, we were terrific. I can't recall another game this season where we have created so many opportunities.
"We scored the goal, hit the bar, their goalkeeper made some terrific saves. From that point of view, we were excellent. Our desire not to go under was incredible as well.
"We just have to be a little bit more ruthless at either end of the park. I think that was the difference.
"Hibs, on their couple of opportunities, were ruthless in their finishing.
"It was a great, great performance from us, we just need to be a little more ruthless in both our attacking and defending."
Falkirk remain four points adrift of Kilmarnock at the foot of the table and have only seven games left to save their top-flight status after their promotion in 2005.
Pressley, who has long insisted his team will stay up, added: "It was disappointing to lose the goals so quickly after us going in front, as we started the game in really positive fashion.
"But they are giving me their lot. I really feel for them, because I don't think the results just now are a true reflection of our performances.
Hibs manager John Hughes, who started a six-match touchline ban, was pleased to return to winning ways ahead of Wednesday's key meeting with Dundee United at Easter Road.
It was only the club's second win in 10 matches as they quickly bounced back from the surprise setback in Dingwall.
Hughes, who kept Falkirk up on the final day last season, said: "Over the last month, there has been a lot of frustration, exasperation, that is nothing against the players.
"I know what needs to be done, I know where I want to go and I'm trying to mould those boys into taking us there.
"It was a big test for us against a side fighting for their lives.
"I felt for the first 20 minutes Falkirk were the dominant side, got their goal, and I think that's what sparked us into life."
Hughes revealed midfielder Merouane Zemmama is to have a scan on his knee that forced his first-half substitution.
Source: Team Talk