Moyes' side took a surprise lead at the Santiago Bernabeu before a flurry of goals from the hosts, courtesy of James Rodriguez, Sergio Ramos and a double from Karim Benzema, saw the home side win 4-1.
However, it was another disappointing afternoon for Bale, who was jeered by Madrid supporters for a second time this season after missing two golden chances for the European champions, with Carlo Ancelotti slamming his critics after the game.
Moyes also added his thoughts on the situation and was fulsome in his praise of the former Tottenham winger despite doing his best to ensure his side kept him at bay on Saturday.
"Gareth Bale is a fantastic player," said Moyes. "He had a couple of chances to score and there is nothing to worry about him. I'm sure he will be someone great."
The Scot was left to lament the gulf in quality between the Champions League holders and his side, while revealing that there will be no last-minute transfer deadline day buys should star striker Carlos Vela's injury prove to be serious.
"We tried to play with the ball," Moyes added." We started the game very well, but there was a big difference in the quality of the teams.
"We don't know what happens to Vela. We will run some tests tomorrow and see what is wrong with him. He is very important to us. We cannot find a substitute in the market, but we will do what we can if he cannot play for a while."
