The Bees ended a run of three defeats thanks to an own goal from Walsall's Joe Broad in a match that was low on quality.
But Allen insisted that it was a huge test of his team's character and rated it as one of their best wins ever.
He said: "That was one of the best performances of the season because you find out more about people when you are losing than when you are winning and everything just flows.
"When you have lost three games in a row you see the character in the team and we showed it today.
"It was a fantastic three points. Today was an important test and we passed it and I am delighted for the players."
The Bees almost went behind in the opening minutes when Jay Tabb headed towards his own goal, but a stunning save from keeper Stuart Nelson to save his blushes.
Brentford were handed victory though when Tabb swung over a cross at the other end that was flicked on by Michael Turner and stabbed into his own net by Broad.
The home side were on top for most of the match but missed a host of chances, with Deon Burton drilling narrowly wide in the first half.
Walsall player-boss Paul Merson was booked for diving early on when the visiting bench were shouting for a penalty, as referee Steve Tanner had an awful game.
He later denied Brentford what looked a certain penalty when livewire winger Alex Rhodes was brought down after 55 minutes.
And he also turned down an appeal when Isaiah Rankin was sent sprawling in the box.
But the Bees hung on for victory as Walsall, despite some nice touches from Merson, failed to create chances.