Forest played poorly in the first half, but Johnson’s thunderous goal in the 14th minute was enough to give them a six-point lead over the bottom two spots.
The Wales attacker rifled the ball into the bottom corner from the outside of the box after Leeds failed to clear a free kick on the right.
“Today’s football performance by our team let me down. We are considering ways to improve “Cooper spoke with Sky Sports.
“We’ve been establishing a team and a sense of identity since the summer, so… step by step.”
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The hosts owed a debutant money.