Since childhood, we have been taught to learn from our mistakes. I believe anyone, including the people at NASA, will do the same. This is the type of thing that happens that eventually lead to us trusting the safety of space travel. We have yet to achieve the pinnacle, and we never will, as it is in our nature to compete and improve. NASA will continue on its path for improving the quality of space travel, and despite this accident being a huge setback, NASA will learn and find out the cause of the explosion, and eventually make people associate "safety" with space travel.
Scientists and engineers put a great deal of time into ensuring the safety of people and the equipment used in space travel. Accidents do happen, but they are rare. Everyone involved in space travel understand that accidents work against advancements in space exploration. They all work very hard to protect people involved and the future of space travel.
From the time astronauts approach the rocket to the time they get back on solid ground, their life is in constant jeopardy. What part of strapping a huge rocket to your back and being thrust into the vacuum of space sounds safe? The smallest flaw in any part of it could cause their deaths.
For the most part space travel is safe. Because space travel involves traveling to very far places where assitance is not readily available, they do a great deal of testing. Fortunatly the explosion involved a test, and no one was hurt, in part because the rocket was unmanned, but they did lose the payload.
The explosion of the SpaceX rocket that was set to launch is a huge setback for the company, but it's not totally unexpected. Space travel requires huge amounts of energy, and that energy is generated through the combustion of dangerous fuels. Anytime we try to send something up into space, there's a chance it will explode before it gets there.
Space travel is amazing, and safer than it used to be, but it's always been and still is risky. Astronauts risk explosions during take off and re-entry as well as complications for being in zero gravity. Collisions with asteroids and other floating bodies are also a risk. Although we can control some of the risk by improving our technology and equipment, but there are risks outside our control.