Real slipped to a 1-0 loss to Atletico on Saturday.
"It was a difficult match because they were well organised defensively and after the goal it was tough because of how they play. In the second half we kept trying, without success," said Bale.
"I went on in the second half and I felt good but I have to improve. But the important thing would have been winning.
"It was a fantastic experience and I have to play better every day to pay back that affection."
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