Part of the issue is that businesses have become so greedy people no longer even want to waste their time negotiating with them. Once I have an offer in hand, I can ask you for some things like a raise, reduced hours, etc. The general response will always be no. At that point I can tell you I have a competing offer in hand and you can then, when you realize you lost leverage too late, attempt to recover the situation. The issue at this point is that you've lost all my trust and I can see indirect retaliation as a reasonable followup should I choose to stay and relinquish my leverage. So it's almost always in my best interest to leave at that point and yes, you "lost."
Alternatively I could have leverage, or maybe I don't, but perhaps when I ask for a promotion or raise you don't immediately discard the discussion or tossed some canned "budgets are tight" argument when margins are visibly fat. You listen and evaluate (and not slowly) and make a decision not based on being cheap but based on actual value. Suddenly, I have a familiar devil I already know and a better setup than I did before. Suddenly you became competitive. No only did you take me seriously and perform an objective evaluation, you followed through with it. You just earned loyalty points which are hard to come by. I expect in the future if I come with another reasonable request, you'll evaluate and attempt to meet it fairly. I suddenly like you.
Now, if I have an offer in hand and I already know you cannot match it because I understand the financials very well and... you really can't afford it, then yes unfortunately you probably did lose. You may be able to compete by making other sacrifices that are less financial in nature but if the offer is significantly higher, unfortunately there's little way I'll stay. Early in my career from my first position I tripled my salary in my first move. My first employer was genuinely great but I knew they couldn't ever reasonably meet that offer so I didn't really even try to negotiate, I just gave them more notice than normal.
Employers probably love when you give them "loyalty points" because they can be substituted for their more tangible "dollar points".