The German also had to deal with a Cristiano Ronaldo tantrum after substituting the Portuguese striker in the second half.
Lacklustre United were outplayed by Brentford in the first half and were indebted to goalkeeper David de Gea but goals by Anthony Elanga, Mason Greenwood and Marcus Rashford capped a muchimproved second-half display.
Ivan Toney then scored a consolation goal for the Bees.
It was a vital win for United and keeps them in the thick of the battle for a top-four finish, but Rangnick was not impressed by what he saw in the opening 45 minutes.
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