The Aston Villa and Argentina goalkeeper let in two long-range strikes from Ola Aina and then by Orel Mangala as his side went 2-0 down at the City Ground.
First, Antony Elanga brushed off Matty Cash before passing to Harry Toffolo.
The Forest star then cleverly set up the on-running Aina, who hit the ball along the ground and into the bottom corner from the edge of the area.
Martinez dived to his right, but wasn't down quick enough to stop the shot from flying into his net.
The 2022 World Cup winner found himself in trouble in the second half too.
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Mangala fired a cut-back towards goal from outside of the area, leaving Martinez scrambling to bat it away.
However, the save fell unkindly for the Argentine, with the ball flying just over the line despite the goalkeeper's best efforts to jump in the net to fish it out.
Martinez won the Yashin Trophy on Monday in Paris, being crowned the best goalkeeper in the world following his Golden Glove at the World Cup in Qatar and, of course, winning the competition with his country.
Fans on X believed Martinez could've done better for both goals, but it was Forest's second in particular that raised eyebrows.
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"And this guy won the Yashin Trophy..." one fan wrote on X.
A second fan said: "Emi Martinez won't want to see this one back."
"A week is a long time in football," a third added.
Forest's two goals were enough for the three points, lifting them eight points of the Premier League drop zone and up to 13th in the league.