New signing James Maddison, taking on departed captain Kane's number 10 shirt, pulled the strings in midfield and provided two assists as Spurs took the lead, fell behind and came back for a point with all the goals in a lively first half.
Postecoglou, who arrived in July as the replacement for Antonio Conte and is the first Australian to manage in the Premier League, took Romero off immediately after the VAR decision despite the player's obvious reluctance to leave.
Bryan Mbeumo equalised 15 minutes later from the penalty spot after Son Heung-Min, taking over from Kane as captain, fouled Mathias Jensen.
The South Korean had an otherwise quiet afternoon and was substituted in the second half while striker Richarlison was even less visible.
Brentford, who finished ninth last season and one place behind Tottenham, beat Spurs 3-1 in their previous encounter at the Tottenham Hotspur stadium last May, with Kane scoring for the hosts.
Persons:
Tottenham Hotspur's Cristian Romero, Paul Childs, Ange Postecoglou, Harry Kane, James Maddison, Cristian Romero, Maddison, Postecoglou, Antonio Conte, Romero, Bryan Mbeumo, Son Heung, Kane, Mathias Jensen, Richarlison, Micky van de, Emerson Royal, Ivan Toney, Alan Baldwin, Clare Fallon
Organizations:
Soccer Football, Premier League, Brentford, Tottenham Hotspur, Brentford Community, Spurs, League, LONDON, Bees, Wolfsburg, Tottenham, Bayern Munich, England, Thomson
Locations:
London, Britain, Sunday, Maddison