Earlier quoted context omitted.
The Anti-Drone strategy in Nagorno Karabakh would have been airstrikes. But the rules of engagement were such that this was not doable. Beyond that, actual Russia support was very limited as punishment for Armenia's reorientation. If this was a full-scale war then the skies would have been full of Su-35s swatting out the TB2s and killing drone operators.
The key to small drone efficiency is that they don't need big airfields which can be bombed. Instead the attacking force will be hard pressed finding hundred separate drone teams hiding in bushes, and forests on the frontline, while flying over enemy AA themselves.
Beyond that, these drones are satellite-guided. You can't control them from bushes and forests. The Bayraktar TB2 that did the vast majority of the damage in Azerbaijan needs to take-off from an actual airfield, too.
What you might be referring to are loitering munitions. Their issue is that they have pretty dumb guidance, so all they are good at is going to predetermined GPS coordinate or homing on radar. The solution is to overrun their positions and use your airforce to shoot them down if they do take-off. They are very slow. It can be expensive to shoot them down but you only have to do so until you overrun their 60km or so range, and for the things in the danger zone you only have to use mobile assets that cannot be targeted via GPS.
In small numbers and without actual drones to help with jamming these loitering munitions are also quite vulnerable to AAA.
There are some long-range loitering munitions, like the IAI Harop. However they can only do radar-seeking missions without a base station and actually do need a base. Additionally munitions like the Harop have a very large radar cross section from anything but the frontal aspect and are thus very vulnerable to detection by modern aircraft radar.