Well, if no physics are used, you could basically monitor if keys are not held down + if the player is not jumping/falling (if you care about vertical speed too) - if both are true, then the player is not accelerating. Without external factors that affect the speed, this would be accurate until the moment when the player reaches the maximum speed (e.g. moving at the maximum velocity, which is constant), perhaps adding a "is speed < maximum speed" check could prevent this.
However, these checks probably would be less efficient than just updating a single variable (e.g. "PreviousTickSpeed").
Then again, none of this should be too important, as drawing processes usually take up most of the CPU / GPU resources (usage commonly said to be around ~90%).