This will always happen if you don't have a daily, weekly or monthly limit of what amount you should gamble with. If you have a limit and you haven't exceed the limit, then you have nothing to worry about even if you lose the first bet.
Your limit can`t protect you from losing, and, as result from fear of losing. It can only make your losing not so critical for your budget.
In your way of planning good idea is to set bet size, depends on your planned budget. You will know that you can lose 5-10-15 bets and it can help to avoid fear.
But if you feel fear from betting just avoid gambling - you don`t get positive emotions from the process, why do you want to torture yourself?
One of the reasons for fear in gambling is placing bets with money that you can't afford to lose and also expecting too much from gambling wins. If a gambler is able to plan a good budget that they can afford to lose and not expect that the outcome of gambling must be a win, I don't think there will be any fear while gambling. When there is fear in gambling, there are two things that need to be done: either one should gamble only with money that they can afford to lose or not gamble at all.