Sergio Perez will race in Brazil but beyond that looks uncertain
Perez started 18th and finished last on the track after collecting a penalty for a false start and then being involved in several clashes with other drivers that left his car bashed and holed.
At the same time, Red Bull lost second place in the constructors' standings to Ferrari despite Max Verstappen leading the drivers' championship.
Asked directly if Perez - whose form has crashed since May - was going to finish the season with Red Bull, Horner offered no words of comfort for a driver who technically has a contract for 2025.
Instead, it sounded like Perez may have raced for the last time in front of his home crowd in F1.
"You know, there comes a point in time that difficult decisions have to be made," said Horner. "We're now third in the constructors' championship.
"Our determination is to try and get back into a winning position but it's going to be a tall order over these next four races."
Horner said Perez would be in Brazil next weekend for the final race of an American triple header, but there was plenty of speculation at the Autodromo Hermanos Rodriguez that a change could be made for the last three rounds.
Horner said Perez's weekend had been 'horrible' with nothing going right for him.
"He knows Formula 1 is a results-based business and inevitably when you're not delivering then the spotlight is firmly on you."
Horner repeated the statement when asked if Perez's seat was at risk, referring to the Mexican as "under-performing" and saying scrutiny was constant.
"As a team we need both cars scoring points and that's the nature of Formula 1," he added.
"We're working with him as hard as we can to try and support him. I think we've done everything that we can to support Checo and we'll continue to do so in Brazil next weekend.
"But there comes a point in time that you can only do so much."