It makes sense to feel like you got a good workout if you're drenched in sweat, about to pass out, and sore for days afterward. Clearly, you pushed yourself to some kind of limit and your body responded in kind. The caloric burn, muscular engagement, and overall exertion level must have been high.
But here's the thing. Just as it's possible to speak a lot without saying anything, it's possible to work out without really exercising. Or, put more specifically, it's possible to be "worked out" without being "trained."
The hallmark of "Training" is working towards something specific. The thing about specific goals is that they sometimes require taking specific steps. Let's say you want 6-pack abs. In this scenario, you're in decent shape but you work in an office and sit at a desk all day. As a result, you suffer from minor back discomfort.
It might seem like dive-bombing the entire midsection all at once will bring to your goal faster. Well, it won't if you get injured. It would be easy to aggravate your back discomfort while doing high-volume situps, even though doing 60 of them leaves you pleasantly drenched in sweat and gasping for air.
So what is the solution? To give up on your goal? Gosh no! It's to take small steps towards building a strong, integrated core so that moving in one direction doesn't cause pain in another.
This might mean having to go slow at first, learn proper core engagement, and strengthening each individual muscle (and the "abs" consists of more than one). But if you really want that blocky 6-pack look, you'll take the time to do what you need to do to get there.
And I haven't even mentioned the steps you'll need to take in the kitchen!
Take any specific goal: down three dress sizes, a 405# deadlift, 10 straight pullups, 17 inch arms. They are great and wonderful goals all right! And each one requires patience to achieve. If they could be done easily, everyone you see would be fast and strong, with cardiorespiratory endurance to spare and little bodyfat to speak of.
So when your trainer tells you go a little slower, take a little longer, use a little more concentration, or do this simpler exercise before jumping to the complex one, listen to him or her and trust that there's a reason for it.
After all, having awesome goals can be very exciting and inspiring, but what's even more inspiring is actually reaching them.