Tottenham have returned to the Premier League's top four after a flurry of goals early in the second half helped them come from behind to beat Brentford 3-2 in a fiery London derby.
Asked whether Maupay's celebration had fired up his players in what was a physical confrontation, Postecoglou was unimpressed.
"I'm not a fan of it. I don't like the whole bravado, pushing people around," he said.
"If you're that brave about things, my players and their players, get into a UFC cage and I'll see how brave they are.
"We're out there to play football and that's what I want our guys to do, focus on playing football.
"They shouldn't get motivated by things that aren't really that important to us."
The 20-year-old right-back fired into the bottom corner in the 39th minute to double the Reds' lead having earlier provided the pass that led to Diogo Jota's opener midway through the first half.
After Darwin Nunez sent a penalty against the post in first-half stoppage-time - one of four times he hit the woodwork - the advantage was extended in the 65th minute when Dominik Szoboszlai headed in from Bradley's cross.
Christopher Nkunku replied before Luis Diaz wrapped things up for Jurgen Klopp's men as they made it 15 league matches unbeaten in their first top-flight outing since the German coach's announcement he is to step down at the end of the season.
A miserable evening for Mauricio Pochettino's Chelsea ended a three-match winning run as they stayed 10th.
Manchester City, who have played a game fewer than Liverpool, returned to second place with their fourth league victory on the bounce - beating struggling Burnley 3-1 at the Etihad Stadium.