The main reason that more internal room is required for a double action revolver than a single action is because of the larger arc that the trigger must travel through in a DA revolver. In a single action revolver, the trigger's only function is to release the hammer, so its arc of travel is relatively short. In most single actions like the Colt SAA or Ruger Blackhawk, the hand (sometimes called the pawl depending on the manufacturer) is connected to the hammer, so it is the arc of the hammer's travel that raises the hand/pawl and thus rotates the cylinder. The trigger itself only has to move very slightly in order to engage the full cock and, if present, half cock notches on the hammer. Because the largest part of the hammer is outside the frame, the internal room needed is quite small.
In a double action revolver, however, the trigger actually accomplishes five different functions: it cocks the hammer, releases the hammer, lifts the hand/pawl, withdraws the cylinder stop, and releases the cylinder stop. The part of the hammer which is inside the frame of a double action revolver is much larger than that of a single action because there are three different parts that it acts upon (hammer, hand/pawl, and cylinder stop). Also the arc of travel required to cock the hammer from the inside is much larger and requires a bigger part than the arc necessary to release the hammer only.