Son, who currently captains Spurs, is representing South Korea in the Asia Cup in Qatar, giving Romero the opportunity to lead the team again in the FA Cup tie against Manchester City.
Romero captained the team during the 2-2 draw against Manchester United two weeks ago, and Postecoglou has been impressed with how the Argentine center-back has handled the additional responsibility.
"There is definitely a void, but with every challenge, there are always opportunities," said Postecoglou. "Romero has truly stepped up in this regard. You can feel it in the team. He knows that Sonny is not here and he understands what Sonny brings on a daily basis."
The Australian manager continued, "Sonny engages with everyone in the building, asking, 'how are you doing?' and Cristian is doing that now. I can see it. In training, he's more vocal than before, and that's the beautiful part of it."
"There is a void because we're missing one of our leaders, but from my perspective, as an outsider, I was waiting to see if anyone would step up or if I needed to intervene. But he has stepped up."
Tottenham currently sits eight points behind Premier League leaders Liverpool. Despite various absences, including Son's and the departures of Pape Sarr and Yves Bissouma for the Africa Cup of Nations, Postecoglou is proud of how the team has regrouped after a challenging November, especially considering it is his first season at the club.
"There's a great feeling within the group right now about the progress we're making," Postecoglou said.
"They understand that due to what we've been through, when someone is missing, we fill that gap and continue until they return. It's been a positive experience for the team's growth."
He added, "We could have easily sailed through the first half of the year, and I'm sure the questions directed at me would have been, 'what happens when we face adversity?' I wouldn't have been able to answer that question.
"I would have had to bluff my way through it, but now I already know. I've witnessed the resilience, and part of that comes from how we've dealt with those absences."