Boss Ian Murray reckons Airdrie produced a complete performance to batter the Bairns and keep the pressure on leaders Cove.
The Diamonds made it 13 games unbeaten in League One with a 4-1 victory, thanks to Callum Smith's deadly double, a Callum Gallagher header and a strike from Hearts loanee Scott McGill.
Leigh Griffiths netted a consolation for Falkirk but it was all about Airdrie as they stayed five points behind rivals Cove - and Murray was blown away by his Diamonds.
It was a game where Smith, Dylan Easton and Adam Frizzell, in particular, turned in another sublime display and Murray beamed: "The boys executed the game plan and tactics perfectly.
"The early goal helped and we had a couple of opportunities after that to increase our lead.
"I don't think I'm being out of order or disrespectful to say it could have been 3-0 or 4-0 at half-time, so that was our frustration.
"But we knew if we went out in the second half and just showed a bit more quality in the final third, which is the hardest thing to do in football, our time would come.
"The whole team was excellent. It's very difficult to pick a standout player.
"It was a complete performance and we just have to keep going to try and catch Cove."
Early on in the day it looked like Lanarkshire rivals Clyde might do the Diamonds a favour when they were drawing 1-1 with 10-man Cove, but Paul Hartley's side didn't suffer from that disadvantage as they too ran out 4-1 winners to stay in command at the summit.
Murray added: "We've been saying it for weeks and months now, we have to appreciate both teams are on fantastic runs.
"Cove will be in the exact same situation as us, checking how the results have gone after the game.
"We won't give up, we just simply won't.
"Regardless of if we take a bump along the way, we'll keep hanging in there until it is impossible for us.
"The players have responded to the challenge brilliantly and I think any doubts people had about this team and handling pressure have been firmly put to bed."
Falkirk boss Martin Rennie, whose side are six points off the promotion spots, said: "In the second half we were making so many mistakes and we got punished for every one of them. It was very disappointing."
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