The Wales international joined the Liga giants for £86 million shortly before the close of the summer transfer window, and is set to make his eagerly-anticipated debut against Villarreal this weekend.
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"Bale is not an absolute world-class player," he told Sky Sports News.
"I know him and I’m very surprised about this transfer fee. Now he has to prove himself.
"I do not think he will make it at Real Madrid.”
The current Azerbaijan boss was quick to praise Arsene Wenger, however, following Arsenal's sensational £40m deadline-day move for Mesut Ozil.
"Congratulations to Arsene Wenger," Vogts added. "Mesut Ozil is the type of player that Arsenal have been waiting for."