Real were held to a 1-1 draw by Olympique Lyon in their last 16, second-leg at the Bernabeu, the venue for May's final, to crash out 2-1 on aggregate.
NEWS: Lyon stun Real at Bernabeu
Asked in an interview with Spanish television whether Chilean Pellegrini would still be in charge next season, Valdano said: "Yes he has a contract, which is why the club's plans are for Manuel to continue being the coach of Real Madrid.
"Pellegrini is the coach of Real Madrid, we respect him, of course, and we trust in his work," he added. "There is still a lot to be done."
Real's latest European failure comes after investment of close to a quarter of a billion euros ($340 million) in players in the summer and the domestic league is now their only chance of silverware this season.
"It's is a sad night because we were very excited about this competition but we are not going to exaggerate the situation on the basis of one match," Valdano said.
In a separate television interview, Pellegrini said his future depended on the club's management board and he planned to continue working.
"It was a very big slip-up," he said. "Tomorrow we have to think about continuing the fight for the league title."
