The Blues arrived in west London off the back of their sub-par 2-1 win over AFC Wimbledon in the Carabao Cup during the week.
A first Premier League win of the season came five days prior as they cruised to a 3-0 win over newcomers Luton Town.
With the international break taking place next week, Chelsea had the chance to continue their progress under the new boss.
However, it was one of Forest's summer signings who proved to be the difference on the afternoon at Stamford Bridge.
Anthony Elanga, who arrived in a £15million deal from Manchester United, scored just three minutes into the start of the second half.
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He was played through on goal by the in-form Taiwo Awoniyi and his shot crawled past Robert Sanchez in the Chelsea net.
Nicolas Jackson had a wonderful chance to level late on but his effort from close-range went over when he should have scored.
Despite Chelsea's efforts throughout the the second half, it was Forest who emerged victorious.
The Blues by no means offered little in terms of chances as Raheem Sterling and Conor Gallagher also came close.
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However, it was a performance that suggests that even though the Blues are stacked with talent, it may still take time to click.
Build-up play will be a promising sign for fans but it's the lack of a clinical finish in the final third that is holding them back.
Forest on the other hand have finally be rewarded for their work as impressive performances against Arsenal and United ended in draws.
They have now made it two wins from four, an impressive record given how tough their start to the season has been.