New signing Michail Antonio scored his second goal in as many games to see off the challenge of League Two side Tranmere Rovers at Prenton Park.
Forest survived spending the majority of the second half with ten men after Michael Mancienne received a second yellow card.
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"This was a proper cup tie, we always felt that Tranmere would stretch us and they did. Once Michael got sent off it became a battle, but we were pleased overall," said assistant manager Steve Wigley afterwards.