Rodrigo Bentancur gave Tottenham the lead after five minutes before Morgan Rogers and Emiliano Buendia scored to secure all three points for the visitors.
Tottenham now sit in sixth place with four wins, two draws, and two defeats from their opening eight Premier League games.
Romero, 27, was expected to start but missed out on a place in the squad due to a “Minor doctor issue, nothing big,” per Thomas Frank.
On whether the defender will be available for the game against Monaco, he added: “I don't know. He could be, he couldn't. I just don't know.
“Right now, if I'm honest, I had one focus I went into the changing room and then I spoke to the players and then I prepared a little bit for Anthony for the questions they're going to have. And then I worry about the players tomorrow.”