Webber has seen his world championship challenge disappear after teammate Sebastian Vettel emerged victorious from the last four grands prix, and Horner believes that will focus the Australian driver's attention on helping Vettel win the drivers' championship.
Horner said: "Mark is a strong competitor and a big team player. I'm quite convinced he will want to see the team achieve its best possible result, and I'm sure as a team player he will do everything to support the team.
"Mathematically it's very difficult for him to win the championship.
"But he's a smart guy, an important part of the team, and I've every confidence he will be doing his best to help the team achieve its objective for the championship."