Believe it or not, there are days when rolling out a mat and getting into a vigorous practice is the last thing diligent practitioners and even yoga teachers feel like doing. I used to get frustrated with myself on days when I neglected to move my body, but over time I have realized that not practicing can be just as much of a yoga practice as plowing through sun salutations.
Which is OK, because yoga is a multifaceted practice not limited to asana or physical postures. As such, flowing and moving through poses does not have to last a certain amount of time or look a certain way in order to be considered a yoga practice. It does not even have to be executed on a mat, and it does not have to last for more than a minute. It may or may not include strengthening muscles, but it will most definitely include paying attention to the breath and body for however long you have.
For example, sometimes after a flight or a long day of running around, I will stand wherever I have space in my apartment, with or without a mat, and stretch my arms overhead. I'll go back and forth for a few side-body bends, then take a gentle forward fold with my hands interlaced behind my back and bent knees. I hold these for a few breaths each, for as long as feels necessary, and then take a moment with my hands pressed together at the center of my chest to say a heartfelt "thank you."