Real spent around 40 million euros to lure the highly rated France striker from Olympique Lyon at the end of the 2008/09 season but under Mourinho the 22-year-old has slipped behind Argentina forward Gonzalo Higuain in the pecking order and questions have been raised about his focus and commitment.
Tuesday's last 32, first leg in Murcia will be a chance for Benzema, who will start the game, and possibly other second-string players like midfielders Pedro Leon, Sergio Canales and Esteban Granero to impress, Mourinho said at a news conference.
"For the players who are not getting as much time on the pitch it's a very important match," said the Portuguese, who joined Real from Inter Milan at the end of last season.
"If a player doesn't show his quality in this kind of match he can't expect to be selected for the weekend," he added.
"This is the pressure they are under and they have a responsibility. A player who doesn't play well tomorrow won't be selected for Saturday it's that simple. I'd rather put players from the B team on the bench."
Asked about Benzema's chances of securing a regular spot in the starting 11, Mourinho said it was mainly Higuain's rich vein of form that was keeping the Frenchman on the bench.
"The level that Higuain is working at he is shutting the door to the others," he said.
"He works for the team and is scoring goals and the reason Benzema is not playing is Higuain.
"Benzema needs to have the mental strength to keep working and he has to take his opportunity and try to shut the door to Higuain.
"We have a system under which it's difficult to have them both playing at the same time. It's not Benzema who is playing badly it's Higuain who is playing well," added Mourinho.
"This is a team and we all work toward the same goal but internally there is a lot of competition."
