water pressure drops when irrigation system is turned on
It sounds like your well is not able to provide the flow rate needed to supply your sprinkler system.
Let's say that your well/pump/plumbing are able to provide 5 gal./minute.  If you exceed that rate then the pressure will drop.  It's unlikely that low water level in the well is the source of your problem as in that case the pump would start sucking air and you would notice the air in the system as it &quot;burps&quot; out.
I'd start by checking your plumbing for suitable sizes of pipes and fittings and see if there are any obvious problems such as way too small pipes.  If that fails to reveal any issues you likely need to engage a well service professional who can evaluate your well and pump and make any recommendations that might correct your problem.
Keep in mind, especially if your well and pump are old, that fixing this may involve replacing the pump, drilling a new well, running a new pipe from the well to the home, etc.  In other words, it may be expensive.