"There was no reason to give a false sense of hope."

I could see how people got that false sense of security.

But the tools can provide a false sense of security.

It gave us a false sense of security to be in touch with the outside world.

They only give a false sense of safety and security.

So you could say that a false sense of security set in.

They want to be the first at doing whatever gives them a false sense of being cool.

If you do, you'll develop a false sense of security.

"How could you not have a false sense of security?"

But you have the false sense that nothing can go wrong.