I'm often fearful as soon as my stock price goes down. How can I cope with this fear?

I would say that the majority of investors find it hard to cope with a short-term loss. When starting out in value investing, it can be difficult to deal with holding a stock when the price is going down. So I understand your concern.
Some investors choose to set stop-loss orders.
The way I feel about setting stop orders is that I’m increasing the likelihood of guaranteeing a loss.
It’s important to remember that you don’t really lose money until you sell a stock. Therefore just because the price goes down, it doesn’t mean that you’ve lost any money and it doesn’t mean that the value of the company has actually gone down.
Price doesn’t = value.
If a stock falls that I bought as a good company at a bargain price, I usually will only consider selling if something drastic has changed in the company that will affect its long term growth and value.
For example, if I look at the stock that’s falling in price, and I see a good company that is facing some temporary issues, then I’ll just hold until the stock is repriced so that its price moves closer to the real value of the company.
Here’s a quote by Warren Buffet:

“The most common cause of low prices is pessimism – sometimes pervasive, sometimes specific to a company or industry. We want to do business in such an environment, not because we like pessimism but because we like the prices it produces.”
 
I hope this info is useful.
-Grant