The Argentine center half retweeted a comment on X about having to arrange his own travel back from international duty.
The tweet in question had stated that Romero was unwell in the lead up to their 1-0 loss to Arsenal in the Premier League on Sunday, in which he committed an error that led to the only goal of the game.
Postecoglou told reporters: “No, (the retweet) was mentioned to me but it wasn’t mentioned to me before the game. I knew nothing about it. The players got back on Thursday and we had a Sunday game.
“No one reported anything other than the usual checks of people coming back from international duty so prior to the game - no one said anything.”
On any health risks for Romero as a result of travel, he added: “As I said, there was nothing before the game that was mentioned to me.”