Davies slid into a challenge with Vincent Kompany but only made contact with the centre-back's knee, which led to an angry reaction from the Belgian international.
Spurs remained with 11 men on the pitch as referee Jon Moss opted to give a yellow, but Gallagher has acknowledged that Davies should have been dismissed.
Gallagher told Sky Sports News: "It's a red card - a nasty challenge. You can understand why Kompany is upset and it didn't get picked up for the severity of the challenge."
City still went on to prevail by a 3-1 scoreline at Wembley Stadium.