I think a lot of people get put off interval training because they run themselves into the ground simply by not recovering enough.
If you're totally shattered by the end of the session (or worse still, before the end), then you haven't been recovering enough.
You'll still get enormous benefit out of interval training even if you take as long as you like over the recoveries, jog, walk, lie down, go to sleep (well, almost), whatever it takes to finish the session running all your reps at an even but hard pace.
You don't even need to time your recoveries and there's nothing wrong with taking extra time if you need it. Pause, rehydrate (a sports drink is a good idea to have to hand), loosen up and go again - when you are ready.
Incidentally, intervals where you recover completely are properly called "repeats" - confusing, huh? But they are still hugely worth doing.
Of course, there is another use for intervals where you try to keep the recoveries short (and probably moderate the pace of the reps), which is to build speed endurance.
But it's got to make a lot more sense when you're not used to interval training to make the most of the recoveries so you can do plenty of controlled, hard running when you get going again.
In short, don't beat yourself up guys. It doesn't make sense.