Shelvey was the first to be sent off for what was deemed to be violent conduct and Dummett then saw red for allegedly denying a clear goalscoring opportunity.
Both incidents resulted in penalties being awarded to Nottingham Forest, but Newcastle 'keeper Karl Darlow saved both efforts.
Newcastle defended admirably for most of the game with nine men, but ultimately lost 2-1 after going 1-0 up when playing with 10.
Both players wil therefore be available for Newcastle's home match against Birmingham City at the weekend.