Scottish boss Moyes was sacked late in his debut season in charge at Old Trafford and Keane feels it could have been avoided if Woodward had acted in a more prudent manner.
"Why give Moyes a six-year contract? He had one transfer window and it's not always down to the manager when players don't come in," Keane said.
"I think Ed Woodward needs to look at himself. He's got to get deals done.
"I think Moyes should have been given more time."
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