What you need to learn to do, is to shift gently and smoothly without looking down. Do not look down. Keep your eyes on the road ahead of you. Also, make absolutely certain the the high and low limiter screws on both your front and rear derailleurs are adjusted properly. If not, your chain could could go into your spokes and sever one or two, or you could throw a chain.
Downtube shifters are a blast, and you don't need more gears than 2x6. Make sure they're clean, adjusted and lubricated.