LaLiga giants Barca have long been a dominant force in European football, but were humiliated 4-0 in Tuesday's Champions League last-16 first-leg tie at Parc des Princes.
Attacking midfielder Draxler, who moved to the French capital in January after a disappointing spell at Wolfsburg, was influential in PSG's victory and scored the second in between a double from the equally brilliant Angel Di Maria.
But the Germany international says there is no reason for him to get ahead of himself amid the adulation.
Speaking to Bild, he said: "I am still Julian.
"I work and live in a world city, I play for a world club, but I still have both feet on the floor."
PSG may have one foot in the quarter-finals, but must still avoid a Barca backlash at Camp Nou in the second leg.
And Draxler says his celebrations after the first encounter were somewhat muted.
"We were eating with my family, the family of my girlfriend and friends," he added.