The academy graduate was involved in two contentious tussles with Ivan Toney, the first seeing the Brentford forward go to ground when attempting to latch onto a long ball.
Moments later, Chalobah prevented Toney from controlling a high ball with the home team player going down under minimal contact from his marker.
The referee at the Brentford Community Stadium took no action in both situations, decisions which have been backed by Gallagher.
Regarding the first incident, Gallagher said Sky Sports: "He gets a little feel of the shirt, there is no doubt about that. What I would say is that it can't be a red card.
"You have to be in possession of the ball, and he is clearly not, or you have to be in a position where you can gain immediate possession of the ball. Once the referee deems it not to be a foul, he is right to play on."
Describing the following occurrence, Gallagher adds: "He is not caught in the face at all. His arm goes across his shoulder. There's a minor brush. Offside was given anyhow."
Chelsea claimed a 1-0 victory against the Bees to retain top spot in the Premier League standings.