Tottenham began life after Harry Kane with an entertaining draw against Brentford on the opening weekend of the Premier League season.
Brentford, who began the league campaign without talisman Ivan Toney, had taken the lead through Yoane Wissa after Bryan Mbeumo's penalty cancelled out Romero's opener.
Spurs have now failed to win on their three visits to the Gtech Community Stadium, where kick-off was delayed by six minutes because of a water supply issue.
When play did begin, Argentina defender Romero opened the scoring with a guided header from debutant James Maddison's fierce free-kick.
It proved to be Romero's final contribution as he was replaced by Postecoglou as a precaution after appearing to complain of a knock to the head in the celebration.
The Bees recovered and won a spot-kick when Spurs' new captain Son Heung-min brought down Mathias Jensen for Mbuemo to convert and stretch his goalscoring run to four consecutive top-flight games.
Wissa was then the beneficiary of Rico Henry's blistering surge down the left-hand side before side-footing the cutback past Guglielmo Vicario, via a deflection off the boot of Micky van de Ven, to dampen their debuts.
Royal scored the pick of the goals with a guided finish in the fifth minute of 11 added on at the end of a thrilling first half.
No Toney, no problems
Thomas Frank's side know they will have to make do without key forward Toney until mid-January after he was banned for eight months for breaking Football Association betting rules.
The England forward was the third top goalscorer in the Premier League last season, behind Manchester City's Erling Haaland and Kane, but they are not showing any signs of missing him.
Brentford won four of the five games they played without Toney last season and, in Mbeumo and Wissa, they have two competent forwards at this level.
Mbuemo took his penalty with aplomb as he wrong-footed Guglielmo Vicario, while Wissa diverted the ball over the line, albeit not with the cleanest strike of his career.
If Mbuemo and Wissa are the finishers, Henry is a potent supplier as he showed his blistering pace to torment Royal on several occasions.
As well as cruising on to his own touch past Royal to cut the ball back for Wissa's goal, he also did brilliantly to beat his man and find Mbuemo at the far post, with the striker unable to divert the ball past Vicario from close range.
Richarlison struggles in central role
Goalscoring pedigree is the most important feature of any team, and Kane's departure will have Spurs fans worried.
Kane leaves the Premier League as Tottenham's all-time top scorer with 280 goals in 435 appearances.
He leaves behind big boots to fill but, in the short term at least, Brazil forward Richarlison looks set to try and answer Postecoglou's call for goals.
Unfortunately for Spurs and their fans, Richarlison did very little to ease their concerns as he cut an isolated figure. In a quiet first half, as Spurs dominated with 66% of possession, the forward touched the ball only 16 times.
Romero was the only Spurs outfield player to touch the ball fewer times (10) before being taken off in the 14th minute.
Maddison, whose arrival from Leicester over the summer was a big coup for Spurs, tried to roll the ball through early on but Richarlison was muscled out of the way and unable to cause a threat.
The same combination linked up in the second half, but this time Richarlison snatched at the shot and fired straight at Burnley's £11m summer signing Mark Flekken in goal.
Time will tell if Richarlison is Spurs' permanent answer to Kane.
Player of the match
MbeumoBryan Mbeumo
Brentford
Squad number19Player nameMbeumo
Squad number11Player nameWissa
Squad number3Player nameHenry
Squad number6Player nameNørgaard
Squad number2Player nameHickey
Squad number22Player nameCollins
Squad number27Player nameJanelt
Squad number8Player nameJensen
Squad number5Player namePinnock
Squad number20Player nameAjer
Squad number30Player nameRoerslev
Squad number13Player nameM Jorgensen
Squad number9Player nameSchade
Squad number1Player nameFlekken
Squad number26Player nameBaptiste
Squad number24Player nameDamsgaard
BBC Sport app: Download to follow all the latest on your Premier League teamLine-ups
Brentford
Formation 5-3-2
1Flekken
2Hickey22Collins5Pinnock20Ajer3Henry
8Jensen6Nørgaard27Janelt
19Mbeumo11Wissa
1Flekken2HickeyBooked at 62minsSubstituted forRoerslevat 72'minutes22Collins5Pinnock20AjerSubstituted forM Jorgensenat 84'minutes3Henry8JensenSubstituted forDamsgaardat 49'minutes6NørgaardSubstituted forBaptisteat 72'minutes27Janelt19Mbeumo11WissaSubstituted forSchadeat 72'minutesSubstitutes
9Schade10Dasilva13M Jorgensen21Strakosha23Lewis-Potter24Damsgaard26Baptiste30Roerslev33YarmolyukTottenham
Formation 4-2-3-1
13Vicario
12Emerson Royal17Romero37van de Ven38Udogie
4Skipp8Bissouma
21Kulusevski10Maddison7Son Heung-min
9Richarlison
13VicarioBooked at 26mins12Emerson Royal17RomeroSubstituted forD Sánchezat 14'minutesBooked at 36mins37van de Ven38Udogie4SkippBooked at 44minsSubstituted forSarrat 75'minutes8Bissouma21Kulusevski10MaddisonBooked at 36mins7Son Heung-minSubstituted forPerisicat 75'minutes9RicharlisonSubstitutes
5Højbjerg6D Sánchez14Perisic18Lo Celso23Porro27Solomon29Sarr33Davies40AustinReferee:Robert JonesAttendance:17,066Live Text
Match ends, Brentford 2, Tottenham Hotspur 2.
Second Half ends, Brentford 2, Tottenham Hotspur 2.
Hand ball by Vitaly Janelt (Brentford).
Corner, Tottenham Hotspur. Conceded by Mads Roerslev.
Emerson Royal (Tottenham Hotspur) wins a free kick in the attacking half.
Foul by Bryan Mbeumo (Brentford).
Attempt blocked. Richarlison (Tottenham Hotspur) right footed shot from the centre of the box is blocked. Assisted by James Maddison.
Attempt missed. Kevin Schade (Brentford) right footed shot from the right side of the box is high and wide to the right. Assisted by Zanka with a through ball.
Attempt blocked. Mads Roerslev (Brentford) right footed shot from outside the box is blocked.
Foul by Destiny Udogie (Tottenham Hotspur).
Bryan Mbeumo (Brentford) wins a free kick on the right wing.
Substitution, Brentford. Zanka replaces Kristoffer Ajer.
Attempt saved. Pape Matar Sarr (Tottenham Hotspur) header from the centre of the box is saved in the top centre of the goal. Assisted by Ivan Perisic with a cross.
Micky van de Ven (Tottenham Hotspur) wins a free kick in the defensive half.
Foul by Rico Henry (Brentford).
Foul by James Maddison (Tottenham Hotspur).
Nathan Collins (Brentford) wins a free kick in the defensive half.
Foul by James Maddison (Tottenham Hotspur).
Mikkel Damsgaard (Brentford) wins a free kick on the right wing.
Substitution, Tottenham Hotspur. Ivan Perisic replaces Son Heung-Min.