First, try to learn to gradually pay more attention with each stage. Stage 1 is usually laid-back and good for warmup, but in stage 2 things start to actually get dangerous. No need to concentrate with all your might, but keep your eyes open. I mean, you keep dying there, what better motivation do you need to pay more attention?
Second, if you tend to die in the same places, pay some additional attention there. Also, use Stage Practice if you don't already. Try to give the early stages a few runs. Can you do a perfect stage run? Do you fail in the same spots? It's a useful tool even if you don't use it regularly.
Last, but not least, even if you fail early on, don't quit. One life lost isn't the end of a run, even if it was early on. Actually, it can jolt you back into shape instead, and you might even do better than usual after that. Just teach yourself not to give up easily. You'd fail the first few times, but you can learn that if you keep going despite the mistakes.
Personally, I have no problem paying just enough attention all the time nowadays. Not to say I never make mistakes, but I'm always ready to bomb if things don't look like they're going my way. And even when things are totally bad, there's always something you can learn from a run and do better next time. Mind you, I wasn't like that when I just started.