The 2-0 defeat away to resurgent Dumbarton on Saturday means Jackie McNamara's men have won just twice in their last seven First Division outings.
Their form rut has seen them drop five points behind league leaders Morton, albeit with two games in hand.
But with Thistle's last win coming way back on December 15 in a 3-2 home triumph over Raith Rovers, Paton warned his team-mates they must find the X factor quickly if they are to continue to challenge for the title.
Paton said: "It was just not good enough. The last four games have not been acceptable – we have not been ourselves.
"Four games without a win is just not good enough for a team which is challenging for a title. So that is going to make the Falkirk game this weekend massive now.
"The bottom line is that we must win that one."
Although Thistle started well at the Bet Butler Stadium and played some free-flowing football, they failed to get past a resolute Sons rearguard for whom keeper Jamie Ewings was outstanding early on.
Dumbarton's work rate began to disrupt Partick's passing game after the break though, and Paton admitted that teams are starting to stifle the Firhill side.
He added: "I don't know if teams are beginning to figure how to play us better or not, but each one of us needs to lift his level of performance.
"Fair play to Dumbarton they stopped us playing, especially after the break, but we have got to do better than that.
"Three points against Falkirk this weekend is vital, we can't afford to slip any further.
"We had a big support down at Dumbarton and we let them down. We need to pay them back at Firhill."
Despite eventually losing, Thistle will take some positives from their loss at Dumbarton after immediately taking a grip on the game.
After six minutes a 20-yard drive from Stewart Bannigan forced Ewings to make a superb tip-over. And with Sinclair on fire on the Jags' left flank, the full-back was creating havoc early doors, setting up Stevie Lawless for a close-range effort that was again well stopped by the impressive keeper.
But with 20 minutes gone disaster struck. A Scott Agnew free-kick was headed on to the post by Alan Lithgow and with Thistle keeper Scott Fox stranded, the ball cannoned into the Jags net via a cruel deflection off Conrad Balatoni, totally against the run of play.
After the break Thistle struggled to regain their fluidity and on 63 minutes the home side doubled their lead, with Steven McDouglas stealing the ball from Balatoni to release a cross that former Celt Bryan Prunty finished at the back post.
It was a hammer blow that Thistle failed to recover from, and with Andy Graham and Lithgow dominating the Sons box, Thistle never looked like fighting back into the game.
Now McNamara must find a way to restore the cutting edge to his side, as although momentum has been lost, Thistle are still well placed to come again.