Yogic breathing is pranayama.
Yogic posture is asana.
You are already practicing pranayama when you practice asana.
What you are looking for is to refine your breathing.
Ujayi breathing is an advanced pranayama technique. There are intermediate breathing techniques that are more useful to a developing yogi.
Some yoga disciplines practice sitting pranayama prior to practicing asana. This tends to refine a yoga practice toward peace, sweetness and calm awareness.
Here’s something to try on your own:
Sitting in a comfortable position with feet firmly on the floor (or in lotus or half lotus, on a pillow or not, depending on hip flexibility and general comfort level), breathe in for four relaxed counts. Breathe out fully, then puff out
a little bit more breath. Suck in your diaphragm (muscle under your ribs feels like sucking in your upper stomach) and hold. When your body signals you (really wants that next breath), allow your breath to come in, it will come in hard. Repeat this process and work up to ten repetitions.
This improves breath control and heightens organic awareness of breath when practicing asanas. Don’t try to do advanced breath techniques yet.
Do allow your (newly heightened) attention to rest on how you breathe with each movement of your asana. Really imagine your breath “going into” the part of your body that is talking to you with each pose. See how your new pranayama ability introduces you more fully to each pose. Enjoy !