The World Cup winner sparked a late Tottenham fightback against Arsenal on Sunday with a goal following an error by Arsenal goalkeeper David Raya.
It could not prevent a 3-2 defeat that left Tottenham's hopes of a top-four finish hanging by a thread, but Romero's display was a highlight for the hosts.
"He was outstanding. He's a World Cup winner and I've just got to get some of what's in him into some of the others," Postecoglou told reporters.
Romero's feisty personality has led to problems since joining the club and he has picked up 22 yellow cards and two reds in his 77 Premier League appearances.
He is clearly a classy performer though and Tottenham will need him if they are to improve next season.
Sunday's defeat summed up Tottenham's season. They dominated at times and played some enterprising football but were picked off all too easily by a clinical Arsenal side who secured the win that kept them ahead in the title race.
"It's disappointing. The outcome was disappointing. We wanted to win today for our supporters and for the club. We didn't do that and whatever I think about the performance it's still the outcome that sits on you," Postecoglou said.
"I thought our general football was good, was decent. We controlled the game for long periods for the most part but we know that. We know we're a team that can do that."
Two of Arsenal's goals came from corners, the first an own goal by Pierre-Emile Hojbjerg and then one from Kai Havertz with Bukayo Saka's goal on the counter-attack in between.
Postecoglou, however, said he was not obsessing about his side's problems in dealing with set-pieces.
"If I thought fixing defensive set pieces was the answer to us bridging the gap then I'd put all of my time and effort into that. But that's not where we're at," the former Celtic manager told reporters.
"I don't think it's about one part of it, I think it's a bigger, broader picture than that, but our defensive set pieces for those two were very poor.
"But there's a lot more than that to fix."
Tottenham remain in fifth place with 60 points from 33 games, seven points behind Aston Villa who have played two games more. Tottenham still have to face Manchester City, Liverpool and Chelsea.
